When a mass m particle is released onto a smooth inclined plane (where the frictional force F=0), it will glide down the slope.
We resolve in the direction of motion in order to get the particle's sliding acceleration.
F=ma,
mg cos(90∘−θ)=ma,
g cos(90∘−θ)=a,
g sin(θ)=a.
How many Newtons is the net force while the block is travelling at a constant speed?
Zero. Newton's first law of motion states that any object travelling at a constant speed experiences no net external forces, hence the total amount of forces acting on the object must be zero. The mathematical expression for an item being under no net external force is Fnet=0 or F=0.
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A square meter of the axon membrane has a resistance of 0.2 ohms. The membrane is 7.5 x 10‐⁹ m thick. What is the resistivity of the membrane?
Answer:
using the formula
Resistance=Resistivity × length/area
Area=1 ,Resistance(R)=0.2ohm ,resistivity(P)=? ,length=7.5×10^-9
R=Pl/A
Pl=RA
P=RA/l
P=0.2×1/7.5×10^-9
P=0.027×10^9
P=2.7×10^7ohmsmeter
The resistivity of the membrane is 2.7×10⁷ ohm-meter.
What is resistivity?
Electrical resistance of a conductor with a unit cross-sectional area and unit length is called resistivity. Resistivity is a distinctive attribute of any material that may be used to compare different materials based on how well they conduct electric currents. Low conductivity is indicated by high resistance.
Mathematically the relation between resistance and resistivity can be written as:
Resistance=Resistivity × length/area
Given parameters:
Area of the membrane: A=1 m²
Resistance(R)=0.2ohm ,
resistivity(ρ)=?
length=7.5×10^-9 m.
Now:
R=ρl/A
⇒ρl=RA
⇒ρ=RA/l
⇒ρ=0.2×1/7.5×10⁻⁹
⇒ρ=0.027×10⁹
⇒ρ=2.7×10⁷ ohm-meter.
Hence, the resistivity of the membrane is 2.7×10⁷ ohm-meter.
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part g a transmitter on the earth's surface radiates sinusoidal radio waves equally in all directions above the ground. an airplane flying directly over the radio station at an altitude of 11.5 km measures the wave from the station to have electric-field amplitude 0.360 v/m. find the magnetic-field amplitude measured by the airplane. express your answer with the appropriate units. templatessymbols undoredoresetkeyboard shortcutshelp bmax
After solving the equation the amplitude of magnetic field is 1.2× 10^-9 T.
What is amplitude of magnetic field?
Amplitude of magnetic field is a measure of the strength of the magnetic field. It is measured in units of Tesla (T) or gauss (G). The magnetic field is produced by electric currents, the movement of charged particles, or the spin of an atomic nucleus. The amplitude of the magnetic field depends on the source, the amount of current, and the distance from the source. The Earth's magnetic field has an amplitude of approximately 30-60 microtesla (0.3 - 0.6 mG). At the surface of the Earth, the magnetic field is strongest near the poles, where it can reach over 65 microtesla (0.65 mG). In space, magnetic fields can reach amplitudes of up to 40,000 microtesla (400 G).
The distance between airplane and transmitter, R = 11.5 km
Amplitude of electric field, E = 0.360 v/m.
Amplitude of magnetic field, B = E/c
= 0.36 /3 × 10^8
= 1.2× 10^-9 T
Hence the amplitude of magnetic field is 1.2× 10^-9 T.
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The magnetic-field amplitude measured by the airplane 1.2× 10^-9 T
What is magnetic field?
The magnetic field is the area where the force of magnetism acts on a magnetic material or a moving electric charge. In order to impose a force on other adjacent moving charges and magnetic dipoles, moving electric charges and magnetic dipoles form a magnetic field.
The maximum field strength of the electric and magnetic fields can be found in electromagnetic waves by measuring their amplitude. The amplitude of the wave determines its energy.
The distance , R = 11.5 km
Electric field amplitude, E = 0.360 v/m.
Magnetic field amplitude, B = E/c
= 0.36 /3 × 10^8
= 1.2× 10^-9 T
So the amplitude of magnetic field is 1.2× 10^-9 T
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What is observation of demonstrating the force of attraction and repulsion between two current parallel carrying conductor
Answer:
The force of attraction and repulsion between two current-carrying parallel conductors can be demonstrated using a simple experiment. To do this, you will need two long, straight conductors, a power source, and a means of measuring the force between the conductors.
First, connect the two conductors to the power source so that they are carrying current in the same direction. Place the conductors parallel to each other, and measure the force between them using a spring scale or other device. You should observe a force of attraction between the conductors.
Next, reverse the direction of the current in one of the conductors, and measure the force between the conductors again. This time, you should observe a force of repulsion between the conductors.
This experiment demonstrates that current-carrying conductors exert a force of attraction on each other when the currents are in the same direction, and a force of repulsion when the currents are in opposite directions. This phenomenon is known as the Lorentz force.
Cynthia's broker charges her a commission of $88 for every $1000 of stock bought or sold. Cynthia bought
2,000 shares of Ombor Medical Supplies at $35.49 apiece. As the price rose and fell, she sold off part of her
holdings. When the price rose to $48.57, she sold 600 shares. The price fell somewhat to $46.10, so she sold
1,150 of her shares. When the price climbed to $53.46, she sold off the remainder of her holdings. How much
profit did Cynthia make in total?
a. $9,889.82
b.
$24.542.00
c. $16,312.06
d. $74,799.58
Please select the best answer from the choices provided
$9,889.82 much profit did Cynthia make in total.
What is Stock?In the financial markets, it can be difficult to tell stocks from shares. Both terms are typically interchangeable in American English when referring to financial equities, more precisely, securities that signify ownership in a public corporation.
The more inclusive, generic term is "stocks." It is frequently used to refer to a portion of ownership in one or more businesses.
In comparison, "shares" has a more precise connotation in everyday speech: It frequently refers to the ownership of a specific business.
Therefore, $9,889.82 much profit did Cynthia make in total.
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Consider the ballistic pendulum collision. The projectile, of mass m, is fired into a large block of mass M Derive a formula for the fraction of the magnitude of kinetic energy lost Express your answer in terms of the variables m and M Evaluate the fraction for m = 18.0 g and M = 380 g . Express your answer using three significant figures..
A massive block of known Mass is struck by the projectile, which has mass m. The amount of kinetic energy wasted as a percentage is 0.955.
Describe mass.A quantitative representation of inertia, the fundamental property of all matter. In essence, it describes the resistance of a body of theory to altering its movement or location in reaction to the applied load. More and more volume a body has, the less the change brought on by an external load is.
The mass formula is what?The average concentration (M), which is a physical property, is the same mass as one mole of a hazardous chemical or the ratio of the quantities of a psychoactive compound to its own amounts of pollutants.
Briefing:kinetic energy lost = change KE/KE
=1-m/(m + M)
=0.955.
momentum,
mv = (m + M)*V
V=m(1/( M + m))v
kinetic energy lost,
ΔKE / KE
= 1-m (1 / (m + M)
ΔKE/KE = 1-18(1/(18+380)
ΔKE/KE = 0.955
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A student is trying to determine the muzzle
velocity (initial) of a bullet that is too fast to
measure directly. The student fires the 0.05kg
bullet into a 4kg block of wood initially at rest.
After the collision, the block, with the bullet
embedded inside moves to the right with a
speed of 1.87m/s right.
before collision:
Pbullet
Pblock
after collision:
Pcombined
kg m/s
kg m/s
kg m/s
How fast was the bullet fired?
m/s
mu + MU = (m + M) V... eq (1)
given:
m=0.05 kg, M=3.5 kg, U= 0 and V=1.82 m/s.
put these numbers to equation (1)
0.05×u +0 =(0.05+3.5)×1.82
u=3.55×1.82 /0.05
u= 6.461/0.05
u=129.22m/s ...(2)
prior to a collision
Bullet: |p|bullet =mu =0.05129.22=6.461 kg/s
|p | block = MU=3.5×0 =0 kg.m/s
After collision
Combining, |p| equals (m+M)V = (0.05+3.5) 1.82 =6.461 kg.m/s.
Equation (2) shows the initial speed of the projectile.
=129.22 m/s.
what is collision?
Collision is defined as the meeting of two or more things with such force that both or all of them suffer harm or have their development significantly slowed.
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Every winter morning when the sun is shining bright, a man living in Montana pulls back the drapes on a large, south-facing window. In this way, he helps heat his home using ________.
a. passive solar
b. active solar
c. photovoltaic
d. conductive solar
e. radioactive solar
Answer:
(b) active solar because the solar radiation passing thru the window will help to heat his room
One mole of oxygen gas is at a temperature of 30°C. If the gas is heated at constant volume until the pressure triples, what is the final temperature?
A. 60°C B. 50°C C. 363 K D. 423 K
The final temperature is 909 K or 636° C.
What is Gay-Lussac's law?According to Gay-Lussac's law, the pressure that a gas (with a given mass and maintained at a fixed volume) exerts varies directly with the gas's absolute temperature.
Initial temperature of the gas: T₁ = 30⁰ C = 273 + 30 K = 303 K.
Initial pressure of the gas = P₁ = P
Final pressure of the gas = P₂ = 3P
Final temperature of the gas: T₂ = ?
Now from Gay-Lussac's law;
T₁/P₁ = T₂/P₂
T₂ = T₁P₂/P₁
= 303 K × 3P/P
= 3 × 303 K
=909 K
Hence, the final temperature is = 909 K = 636° C.
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A roller coaster car is released from rest at the top of the first rise and then moves freely with negligible friction. The roller
coaster shown in Fig. P7.62 has a circular loop of radius R in the vertical plane. (a) First, suppose the car barely makes it around the
loop; at the top of the loop the riders are upside down and feel weightless. Find the required height of the release point above the bottom
of the loop, in terms of R. (b) Now assume that the release point is at or above the minimum required height. Show that the normal force
on the car at the bottom of the loop exceeds the normal force at the top by six times the weight of the car. The normal force on each rider
follows the same rule. Such a large normal force is dangerous and very uncomfortable for the riders. Roller coasters are therefore not
build with circular loops in vertical planes. Figure P5.24 and the photograph on page 134 show two actual designs.
a) Height is calculated as = 5R/2 b) It is shown that the normal force on the car at the bottom of the loop exceeds the normal force at the top by six times the weight of the car.
What is meant by normal force?The force that surfaces exert to prevent solid objects from passing through each other is known as the normal force .
a) At point A, PE = m g h
At point B, PE = 1/2 * m * (vB)²
At point C, PE = m(vC)²/R - mg
m is mass vB is velocity at B
vC= √mgR/m = √gR
For conservation of energy at point C and B
1/2 * m * (vB)² + 1/2 * m * (vC)² + mg (2R) ( height of c = 2R)
(vB)² = gR + 2(2gR)
So, vB = √5gR
Conservation of energy between point A and B,
1/2 * m * (vB)² = mgh
Height, h = 5R/2
b) Normal force at topmost point C is
= m(vC)²/R - mg
Normal force at bottom point B is
= mg + m (vB)²/R
NB = mg + m(5gR)/R
= 6 mg
Therefore, we can say that NB > NC
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consider the follwing discussion between two students working on this tutorial regarding the relationship between parallax angle and the distance we measure to a star
Due to the fact that a star's parallax angle and distance are inversely related, I concur with student 2 and disagree with student 1. The farther away the star is, the smaller the parallax angle is.
Student 1: That's not necessarily true. It's true that the triangle in the diagram would be pointier for a star that is farther away, but the parallax angle depends on the ratio of the distance between the Earth and the star to the distance from the star to the edge of the solar system.
Student 2: But if the star is farther away, then the distance between the Earth and the star will be larger, which means the parallax angle will be smaller.
Student 1: Not necessarily. Remember that the distance from the star to the edge of the solar system is also increasing. If the distance from the star to the edge of the solar system increases more quickly than the distance between the Earth and the star, then the ratio of these two distances will decrease, which means the parallax angle will actually increase.
Student 2: Oh, I see what you mean. So it's possible for the parallax angle to increase as the distance to a star increases.
Student 1: That's correct. It's important to consider both the distance between the Earth and the star and the distance from the star to the edge of the solar system when determining the parallax angle.
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Question- Consider the following debate between two students regarding the relationship between parallax angle and the distance we measure to a star.
Student 2: If we drew a diagram for a star that was much more than 1 parsec away from us, the triangle in the diagram would be pointier than the one we just drew in Part II. That should make the parallax angle smaller for a star farther away.
Describe what the motion of the rigid system will be if:
a. The first condition for equilibrium is not satisfied.
b. The second condition for equilibrium is not satisfied.
c. Neither condition for equilibrium is satisfied.
The motion of the rigid system will be (a) linear (b) rotational (c) both linear and rotational
The first condition for equilibrium states that the body must have a net force of zero. This means that when the net force acting on a body is not zero the body will continue to move in a straight path and the motion of the rigid body will be linear.
The second condition for equilibrium states that the body must have zero net torque acting on the body for achieving equilibrium. torque is the rotational equivalent of force. Therefore, when the net torque is not zero, the rigid body keeps rotating which leads to a rotational motion.
When both the conditions of equilibrium are not satisfied the rigid body does not achieve the static equilibrium.
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Can anyone tell me what is new about atomic theory over the last 23 years?
Answer:
The modern atomic theory establishes the concepts of atoms and how they compose matter. Atoms consist of negatively charged electrons around a central nucleus composed of more massive positively charged protons and electrically neutral neutrons. The atomic model changes over time because the atomic model was based on theories and discoveries.
Explanation:
I hope it helps
What happens when a loop of wire turns between two permanent magnets in
a generator?
A. A current flows through the loop of wire.
B. Mechanical energy transforms into electromagnetic radiation.
C. Electrical energy transforms into mechanical energy.
D. A current flows through the permanent magnets.
Answer:
A. A current flows through the loop of wire.
Explanation:
When a loop of wire turns between two permanent magnets in a generator, a current flows through the loop of wire. This is because the movement of the wire through the magnetic field of the permanent magnets causes the electrons in the wire to move, which creates an electric current. This process is known as electromagnetic induction, and it is the principle behind the operation of generators.
at one particular moment, a 17.0 kg toboggan is moving over a horizontal surface of snow at 4.40 m/s. after 6.75 s have elapsed, the toboggan stops. use a momentum approach to find the magnitude of the average friction force (in n) acting on the toboggan while it was moving.
The magnitude of the provided average friction force F (in n) which is acting on the toboggan during it was moving is 8.66 N
What is a toboggan in the USA?Toboggan is a long flat-bottomed light sled composed usually of thin boards curved up at one end with usually low handrails at the sides. : a downward course as well as a sharp decline.
Solution:Given:
vi = 4.1 m/s
vf = 0
Δv = v final - v initial
= 0 - 4.1 = -4.1 m/s
Δ momentum i.e mΔv = (19 kg).(-4.1 m/s)
= 77.9 kgm/s
The average friction force (Ff) takes 9 seconds to take the toboggan to a end point, hence, impulse = Ft
= Ff(9)
Impulse is = Δ momentum, so
Ff(9) = 77.9;
Ff = 8.66 N
Is a beanie and a toboggan the same thing or not ?Touque, Toque and Tuque is in fact the same wool which has a Beanie with three distinct spellings. And at last but not at least in the southern American states , Toboggan is the name used for a wool knitted hat that is worn during the colder months of the year.To know more about toboggan visit
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A wheel is rotating about an axis that is in the z-direction. The angular velocity ωz is -6.00 rad/s at t = 0, increases linearly with time, and is +4.00 rad/s at t = 10.0 s. We have taken counterclockwise rotation to be positive.How long is the time interval during which the speed of the wheel is increasing?
The time interval during which the speed of the wheel is increasing is 4 s.
What is angular acceleration?The temporal rate at which angular velocity changes is known as angular acceleration. The standard unit of measurement is radians per square second.
The angular velocity at time t = 0, is ω₁ = - 6.00 rad/s.
The angular velocity at time t = 10.0 s, is ω₂ = +4.00 rad/s.
Angular acceleration of the wheel = change in angular velocity /time interval
= ( 4.00 - (-6.00))/10 rad/s²
= 1.0 rad/s²
Hence, angular velocity becomes zero at time = ( 0 - ( -6))/1.0 s = 6 s.
So, during t = 0 to t = 6s, the clockwise angular velocity of the wheel decreases from 6.00 rad/s to 0.00 rad/s and during t = 6s to t = 10s , the counterclockwise angular velocity of the wheel increases from 0.00 rad/s to +4.00 rad/s.
Hence, the time interval during which the speed of the wheel is increasing is = 10 s - 6 s = 4 s.
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suppose that a star has a spectrum that includes red, blue, and violet lines spaced in the pattern of the lines from hydrogen but the violet lines are at 424nm and 400nm instead of the usual 434nm and 410nm. from this evidence, you can conclude that the star is
Star has a spectrum that includes red, blue, and violet lines spaced in the pattern of the lines from hydrogen but the violet lines are at 424nm and 400nm instead of the usual 434nm and 410nm. from this star is Moving towards us.
Information about a star's temperature, chemical make-up, and inherent luminosity can be found in its spectrum. A series of photographs taken at various wavelengths of the slit in the star's light make up spectrograms produced by slit spectrographs. Astronomers can identify an element by its spectral lines, as well as its temperature and density within the star. The magnetic field of the star can also be shown via the spectral line. How quickly the material is travelling can be determined by the line's width. This teaches us something about the winds in stars. The object is also referred to as the "Seven Sisters" and Messier 45, and its English name comes from a Greek tale. The Pleiades are seven of Atlas, the Titan deity, and the Pleiades' daughters.
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explain the difference between a ligand-gated k channel and a voltage-gated k channel. match the words in the left column to the appropriate blanks in the sentences on the right. make certain each sentence is complete before submitting your answer. resethelp 1. the ligand-gated channel opens or closes in response to blank .target 1 of 2 2. the voltage-gated channel opens or closes in response to blank .
The voltage-gated ion channels allows permeation of only one type of ion whereas, ligand-gated channels are less selective and allows permeation of two or more types of ions via the channel pore.
What is the difference between ligand-gated and voltage gated K channels?Ligand-gated ion channels are integral membrane proteins that contain a pore which allows regulated flow of selected ions across plasma membrane. Voltage-gated potassium channels are transmembrane channels specific for potassium and are sensitive to voltage changes in the membrane potential of cell .
1. Ligand-gated channel opens or closes in response to blank the binding of a ligand.
2. Voltage-gated channel opens or closes in response to differences in membrane potential.
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A 12-N net force
acts on a 4-kg jug of water. What is the
resulting acceleration of the jug? Show your
calculations.
Answer:
The resulting acceleration of the jug is 3 m/s^2.
Explanation:
To calculate the resulting acceleration of the jug, we need to use the equation F = ma, where F is the force applied to the object, m is the mass of the object, and a is the acceleration of the object.
Plugging in the values given in the question, we get:
F = ma
12 N = (4 kg) * a
Solving for a, we get:
a = F/m
a = (12 N) / (4 kg)
a = 3 m/s^2
Therefore, the resulting acceleration of the jug is 3 m/s^2.
Three particles having charges of equal magnitude q are fixed at the conrners of an equilateral triangle as shown. two of the charges are negative: the other is positive. which of the following vectors best represents the direction of the resultant electric field at point p, the center of the triangle?
Vector B of the following vectors best represents the direction of the resultant electric field at point p, the center of the triangle.
What is vector?A quantity or phenomenon that has two independent properties i.e magnitude and direction is named as vector.
At the middle, where it is zero, one can see that the three charges each produce cancelling fields thanks to symmetry.In addition to the triangle's center, the second panel of the picture shows three additional sites in the middle of each triangle leg where E=0, however they are more challenging to calculate analytically.Adding the electric field vectors resulting from each of the two lower point charges will yield the electric field at point P.
E = E1+ E2.
According to the bottom panel of the picture, a point charge's electric field has the formula E = kr2qr.
E =k ea2q uphill and to the right at 60, and E2 =kea2q upward and to the left at 60.
Therefore, E= E1 + E2 = kea2q[(cos60i+sin60j) + (cos60i+sin60j)] = kea2q[2(sin60j)
= 1.73kea2qj. i.e vector B
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EXPLAIN THE MEASUREMENT PRINCIPLE OF ATOMIC SPECTROMETERS
Atomic absorption spectroscopy, often known as AAS or AA spectroscopy, is one of the earliest methods for elemental analysis to be established for the market.
What is Atomic Spectrometer?The analytical method known as flame atomic absorption spectroscopy (Flame AAS or FAAS) was first commercially released in the 1960s after being invented in 1952.
The method has been well-liked ever since for its dependability and simplicity. AAS is an analytical method for figuring out how much of a particular element is in a sample. It is based on the idea that atoms (and ions) may absorb light with a certain, distinct wavelength.
The atom absorbs the energy (light) when it is present at this particular wavelength. By absorbing energy (light) at a certain wavelength, an electron is stimulated from the ground state to a higher energy level.
Therefore, Atomic absorption spectroscopy, often known as AAS or AA spectroscopy, is one of the earliest methods for elemental analysis to be established for the market.
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A wire carrying a 30.0 -A current bends through a right angle. Consider two 2.00 -mm segments of wire, each 3.00 cm from the bend (the figure ).uploaded imageA) Find the magnitude of the magnetic field these two segments produce at point P, which is midway between them.
B) Find the direction of the magnetic field at point P.
A) The magnitude of the magnetic field these two segments produce at point P is 1.95 nT B) Direction of the magnetic field is into the page.
What is Biot - Savart's law?An equation that describes the magnetic field generated by a constant electric current is called Biot –Savart law.
A) Given; A0 and B0 = 3cm
I= 30 A and l= 2mm
Bio Savart's law;
dB= μIdl sinФ/4πr
Ф = 45° as ΔAOB is an isosceles triangle and Q is the angle between I dL and r.
dB at point P due to 2mm is;
dB= [μIdl sin45°/4πr][1/(AP)² + 1/(BP)²]
= [μIdl sin45°/4πr] [1/(1/2 AB)²+ 1/(1/2 AB)²]
dB= [μIdl sin45°/4πr] [ 8/ (AB)²]
=[(4π * 10^-7 * 30 *2 *10^-3*1/√2)/ 4π] * 8/18
= 1.948 * 10^-9 T
dB = 1.95 nT
B) Direction of the magnetic field is into the page.
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DUE TODAY MIDNIGHT PLEASE HELP!!!!
Describe the process involved in the tip to tail addition of vectors.
Via moving one vector so that its tail sits on the tip of the first vector, you may add by the tip-to-tail approach. New vector drawn from first vector's origin to the second vector's arrow is the resulting vector, A+B, or the sum of the two.
What is the process of vector addition?The head of the first vector must meet the tail of the second vector in order for two vectors to be added together, according to the triangle law of vector addition. We may thus acquire the resulting sum vector by connecting the head of the second vector to the tail of the first vector.The vector's terminal point is the arrow's tip, and its starting point is the arrow's tail. A vector whose magnitude is 0 is known as the zero vector. The only vector without a clear direction is this one.The parallelogram law of vector addition and the triangle law of vector addition are the two different forms of vector addition.Learn more about vector addition refer to :
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When an RLC-circuit is connected to a constant voltage E at time t=0, the current I in the circuit can be solved from the differential equation L⋅d^2I/dt^2+R⋅dI/dt +I/C=0 Where resistance R, inductance L and capacitance C are constants. Solve the equation with the initial conditions I(0)=0 and dI/dt(0)=E/L and assuming that (R/2L)^2−1/LC<0 I(t)=?
By dividing each side of the voltage triangle by its current, I, an impedance triangle for a series RLC circuit can be created. The source voltage is equal to I*Z, the voltage across the two reactive elements is I×X = I×XL – I*XC, and the voltage drop across the resistive element is equal to I*R.
What RLC-circuit is connected to a constant voltage?At resonance, the impedance, Z, is at its lowest value, (=R), because the current flowing through a series resonance circuit is the product of voltage divided by impedance.
Therefore, the circuit current will be at its maximum V/R value at this frequency.
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In the annual battle of the dorms, students gather on the roofs of Jackson and Walton dorms to launch water balloons at each other with slingshots. The horizontal distance between the buildings is 35.5 m, and the heights of the Jackson and Walton buildings are, respectively, 15.5 m and 22.5 m. Ignore air resistance.
(a) The first balloon launched by the Jackson team hits Walton dorm 2.2 s after launch, striking it halfway between the ground floor and the roof. Find the direction of the balloon's initial velocity. Give your answer as an angle measured above the horizontal.
(b) A second balloon launched at the same angle hits the edge of Walton's roof. Find the initial speed of this second balloon.
The basic kinematic equations for horizontal and vertical motion are as follows:
s = v₀t + ¹/₂at²
Horizontal motion is:
x = v₀ₓt + ¹/₂aₓt²
x = v₀ₓt
x = v₀ cosαt
Because there is no air resistance: x = v₀ cosθt
Vertical motion is:
y = v₀[tex]__y[/tex]t + ¹/₂a[tex]__y[/tex]t²
y = v₀ sinαt - ¹/₂gt²
Solve both for the velocity trigonometric function term as follows:
y = v₀ sinαt - ¹/₂gt²
v₀sinαt = ¹/₂gt² + y
v₀sinα = ¹/₂gt² + y/t
and
x = v₀ cosαt
v₀cosα = x/t
Now divide these two equations and we get
v₀sinα/v₀cosα = tanα [tex]=\frac{1/2gt + \frac{y}{t} }{\frac{x}{t} }[/tex]
tan α [tex]= \frac{1/2gt + \frac{y}{t} }{\frac{x}{t} } = \frac{gt^2}{2x} + \frac{y}{x}[/tex]
tan α [tex]= \frac{gt^2}{2x} + \frac{y}{x}[/tex]
Enter a value, x is the distance between the boarding 35.5 m, and y is the difference between the launch height and the drop point. The launch height is 15.5 m and the landing height is 11.0 m, so y = -4.5 m. Finally, we are told the projectile travel time is 2.2 s.
tan α [tex]= \frac{gt^2}{2x} + \frac{y}{x}[/tex]
tan α [tex]= \frac{(9.8)(2.2)^2}{2(35.5)} + \frac{-4.5}{35.5}[/tex]
tan α [tex]= 0.668 - 0.126[/tex]
tan α [tex]= 0.542[/tex]
α = tan⁻¹ 0.542
α = 28.4°
For the second launch, y₂ is +7.0 m launch altitude is still 15.5 m, but the deployment altitude is now 22.5 m, and x is still 35.5 m. The angle remains 28.4°. This time we don't know the flight time or initial velocity we are asked to find. Using horizontal distances, we can solve for time.
x = v₀.cosα.t
t² = x/v₀.cosα
Now do it for y₂:
y₂ [tex]= v_0sin(\alpha) t - 1/2gt^2[/tex]
y₂ [tex]= v_0sin(\alpha) (\frac{x}{v_0cos(\alpha)} ) - 1/2g (\frac{x}{v_0cos(\alpha)} )^2[/tex]
y₂ [tex]= x tan (\alpha ) - \frac{gx^2}{2v_0cos(\alpha)^2}[/tex]
[tex]\frac{gx^2}{2v_0cos(\alpha)^2} = x tan (\alpha ) - y_2[/tex]
We need to solve v₀:
[tex]\frac{gx^2}{2v_0cos(\alpha)^2} =\frac{1}{ x tan (\alpha ) - y_2}[/tex]
2v₀cos (α)² [tex]= \frac{gx}{ x tan (\alpha ) - y_2}[/tex]
v₀² [tex]= (\frac{1}{2cos(\alpha)^2} ) \frac{gx}{ x tan (\alpha ) - y_2}[/tex]
v₀² [tex]= (\frac{x^2}{cos(\alpha)^2} ) \frac{g/2}{ x tan (\alpha ) - y_2}[/tex]
v₀² [tex]= (\frac{x}{cos(\alpha)^2} ) \sqrt{ \frac{g/2}{ x tan (\alpha ) - y_2}}[/tex]
Now we can enter values:
v₀² [tex]= (\frac{x}{cos(\alpha)^2} ) \sqrt{ \frac{g/2}{ x tan (\alpha ) - y_2}}[/tex]
v₀² [tex]= (\frac{35.5}{cos(28.4^0)} ) \sqrt{ \frac{9.8/2}{ 35.5 tan (28.4^0) - 7.0}}[/tex]
v₀² = 40.386 [tex]\sqrt{\frac{4.9}{12.17} }[/tex]
v₀² = 40.386 (0.634)
v₀² = 25.62 m/s
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Analyze physical activities from which derived cardiovascular activity and one strength training activity of moderate to vigorous intensity that can be performed by a person that works out 3 a week doing a of exercises the gym Explain why you chose these activities adults, and briefly describe the long-term of each activity
The physical activities from which derived cardiovascular activity and one strength training activity of moderate to vigorous intensity that can be performed by a person is by jogging, running etc.
What is Exercise?This is referred to as a type of physical activity which helps to keep am individual fit and improves the overall being snd examples include running, squatting etc.
Running was chosen as a form of activity which can be used as a form of cardiovascular activity and strength training activity of moderate to vigorous intensity.
A long-term of running is that it helps to strengthen the muscles and bones which are present in the individual and also improves the cardiovascular fitness which is therefore the reason why it was chosen as the correct choice.
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in 2021, which of the following miscellaneous deductions remain deductible, and are not completely disallowed, although they may have been allowed as deductions subject to the 2 % percent of adjusted gross income (agi) limitation
Miscellaneous deductions subject to the 2% limit fall into the following three categories:
Un-reimbursed Employee ExpensesTax Preparation Fees Other expensesWhat are miscellaneous tax deductions?
Other individual deductions are deductions subject to the 2% Adjusted Gross Income (AGI) limit. You may claim certain expenses as personal deductions on Schedule A (Form 1040), Schedule A (1040-NR), or as income adjustments on Forms 1040 or 1040-SR.
In general, nonresident aliens in one of the eligible employment categories are entitled to deductions so long as they are directly related to income effectively related to the pursuit of trade or business in the United States.
Miscellaneous deductions subject to the 2% limit fall into the following three categories:
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A ladder 25 feet long is leaning against the wall of a house. The base of the ladder is pulled away from the wall at a rate of 3 feet/sec. How fast is the top of the ladder moving down the wall when the base of the ladder is 7, 15, and 24 feet from the wall?
The velocity of the ladder when the base of the ladder is 7, 15, and 24 feet from the wall is -0.875, -2.25, and -10.286 respectively.
Given, the length of the ladder= 25 ft
Let x be the distance between the wall and the ladder and h be the height of the ladder from the ground
x² + h² = (25)²
x² +h²= 625
h²= 625- x²
h= [tex](625- x^{2})^{1/2}[/tex]
[tex]\frac{dh}{dx}[/tex] = [tex]\frac{1}{2}[/tex] [tex](625- x^2)^{-1/2} * (-2x)[/tex]
[tex]\frac{dh}{dx}[/tex] = [tex]\frac{-x}{\sqrt{ (625-x^2)}}[/tex]
We have dx/dt= 3 ft/sec
Therefore, by applying the chain rule, we can get the value of dh/dt as:
dh/dt= dh/dx *dx/dt
=[tex]\frac{-x}{\sqrt{ (625-x^2)}}*3[/tex]
=[tex]\frac{-3x}{\sqrt{ (625-x^2)}}[/tex]
Now substituting the different values of x in the acquired equation
When x= 7, dh/dt= [tex]\frac{-7}{8}[/tex] ft/sec= -0.875 ft/sec
When x= 15, dh/dt= [tex]\frac{-9}{4}[/tex] ft/sec= -2.25 ft/sec
When x= 24, dh/dt= [tex]\frac{72}{7}[/tex] ft/sec= -10.286 ft/sec
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the sun goes down, and over all these barren reaches by the tide such unelusive glories fall, i almost dream they yet will bide 5until the coming of the tide
The passage is describing the beauty of Acadie, a place that is home to the speaker. This passage is from Bliss Carman's "LOW TIDES" .
The sun is setting, and the speaker is captivated by the beauty of the landscape, which is enhanced by the unelusive glories of the tide. The speaker also reflects on a beloved face being gone for a long time and is moved by a grievous stream, which meanders through the fields of Acadie as if it is trying to figure out why the beloved face is gone. The speaker almost dreams that the beauty of the place will remain until the beloved face returns. The passage conveys a sense of longing and hope for the beloved to come back to Acadie.
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A box of mass m slides up a ramp with initial velocity +0. The kinetic friction force on the box has magnitude f. Which of the following is a correct equation that could be used to determine the acceleration a of the box? (A) -f=ma (B) mg sin 0 - - F=ma (C) f-mg sino 0 = ma
(D) -f-mg sino 0 = ma
The equation that could be used to determine the acceleration a of the box is (-f-mg sin 0 = ma)
What is kinetic friction force on inclined plane?If the direction of motion of the mass is up the plane, then the frictional force F will act down the plane.
Normal force N is exerted on the body by the plane due to the force of gravity i.e. mg cos θ. These two will be equal hence cancelled out.
Here, according to the question,
Box is moving up so, Force of friction is acting downwards and mg sin 0 is also acting downwards. Both are acting against the motion of the box so both terms will be negative i.e. (-f) and (-mg sin 0)
We know resultant force is equal to (ma)
So, (-f) + (-mg sin0) = ma
-f - mg sin0 = ma
The equation that could be used to determine the acceleration a of the box is (-f-mg sin 0 = ma)
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A(n) 0.298 kg soccer ball approaches a player horizontally with a speed of 15 m/s. The player illegally strikes the ball with her hand and causes it to move in the opposite direction with a speed of 17 m/s..
What is the magnitude of the impulse de- livered to the ball by the player? Answer in units of kg m/s.
The magnitude of the impulse delivered to the ball by the player is -9.536 kg-m/s
How do you calculate the magnitude of the impulse delivered by the player?Given that,
Mass of a soccer ball, m = 0.298 kg
Initial speed, u = 15 m/s
Final speed, v = -17 m/s (negative as it is in opposite direction)
(a) Impulse = change in momentum
J = 0.298 × (-17 -15)
J = -9.536 kg-m/s
Therefore the magnitude of the impulse delivered to the ball by the player is -9.536 kg-m/s.
What is the formula for the impulse's magnitude?The object's change in momentum is equal to the impulse it experiences. The formula for magnitude of impulse is F • t = m • v. When two objects collide, an impulse occurs, which both causes and equals the change in momentum.
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