vector u has a magnitude of 20 and direction of 0°.vector v has amagnitude of 40and a direction of 60°.find the magnitude and direction of the resultant
Addition of vectors:
vector u
has a magnitude of 20 and a direction of 0º with respect to the horizontal, vector v has a magnitude of 40 and a direction of 60º with respect to the horizontal.
a) Find the magnitude and direction of the resultant to the nearest whole
number.
Vector Sum:
The resultant of two vectors is simply the vector sum of the vectors. There are a handful of ways to present the resultant factor; the notation that shows the vector magnitude and direction is called the polar vector notation. An example of a vector presented in polar vector notation is
a∠θ where a is the magnitude and θis the angle that the vector makes with the horizontal axis.
Answer and Explanation:
Let's first present the vectors in rectangular vector notation.
For the vector →u of magnitude 20 and direction 0∘ to the horizontal axis, the vector is →u=^i20.
For the vector →v
of magnitude 40 and direction 60∘ to the horizontal axis, the vector is →v=^i40cos60∘+^j40sin60∘.
The resultant vector →w is the vector sum of the vectors, i.e.
→w=→u+→v
=^i20+^i40cos60∘+^j40sin60∘
=^i(20+40cos60∘)+^j(40sin60∘)
=^i40+^j20√3
For a vector ^ix+^jy, the magnitude of the vector is √x2+y2 and the direction above the horizontal axis is θ=tan−1(yx).
Let's use the formulas:
|→w|∠θ=√(40)2+(20√3)2∠tan−1(20√340)≈52.9∠40.9∘
The magnitude of the vector is about 53 units in the direction 41-degrees above the horizontal axis.
The magnitude of the resultant vector would be 60 units, and its direction will be 0°.
To find the magnitude and direction of the resultant vector when adding vectors u and v, we can use vector addition formulas:
Magnitude of the Resultant Vector (R):
R = √(u^2 + v^2 + 2uv * cosθ)
where:
u = magnitude of vector u (20)
v = magnitude of vector v (40)
θ = angle between vectors u and v (60°)
Plugging in the values:
R = √(20^2 + 40^2 + 2 * 20 * 40 * cos(60°))
≈ √(400 + 1600 + 1600)
≈ √3600
= 60
Direction of the Resultant Vector (θR):
Use the Law of Cosines to find the angle θR between the resultant vector R and vector u:
cosθR = (v^2 + R^2 - u^2) / (2 * v * R)
Plugging in the values:
cosθR = (40^2 + 60^2 - 20^2) / (2 * 40 * 60)
= (1600 + 3600 - 400) / 4800
= 1
Since cos(0°) = 1, we have θR = 0°.
So, the magnitude of the resultant vector is 60 units, and its direction is 0°.
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Can someone help me with one through seven I will mark you the brainly
Answer:
1. F = M x A
2. Force
3. 2nd Law: Force
4. a, b, c (in order)
5. 3rd Law: Action and Reaction
6. b, c, a (in order)
7. 1st Law: Inertia
1. F=ma
2. Force
3. Second law
4. a)first
b)second
C) third
5. Third
6. a) second
b) third
C) first
7. First
Ce unitate de masura are indicele de REFRACTIE?
Answer:se obesrva ca indicele de refractie NU are unitate de masura, este adimensional. Se exprima print-un raport, de exemplu 4/3, 1,5 etc.
Explanation:
Which of the following would require more energy to heat it from 10°C to 20°C?
a. 200 kg of water
b. 200 kg of aluminum
C. 100 kg of steel
Answer:200kg of water
Explanation:
Hey guys <3
I need some help with this performance task,, physics isn’t my strongest subject so help is much appreciated :)
(2/9 parts)
Answer:
2)Electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field. Electric charge can be positive or negative (commonly carried by protons and electrons respectively)
springs can stretch; so can different materials, including
Which statement best describes a physical change?
A. Changes can occur to certain chemical properties of the substance, but the overall shape of the substance will remain the same.
B. Changes can occur to certain physical properties of the substance, but the overall shape of the substance will remain the same.
C. Changes can occur to physical properties of a substance, but the chemical composition of the substance remains the same.
D. Changes can occur to chemical properties of a substance, but the chemical composition of the substance remains the same.
Answer:
c. changes can occur to certain physical properties
Explanation:
got it right on test
.)
What would the TABLE pane corresponding to the 2D MAP shown below look like?
latitude
30.2°
30°N
29.8°N
29.6°N
longitude
90.40
90.2°
90°W
89.8°
longitude : 89.6 W
Answer:
the correct answer is A the first map
trust i got a 100
Explanation:
Answers are the following:-
1. 33°N latitude, 112°W longitude ⇒ Phoenix, Arizona
2. 35°N latitude, 78°W longitude ⇒Raleigh, North Carolina
3. 46°N latitude, 96°W longitude ⇒ Fargo, North Dakota
4. 45°N latitude, 122°W longitude ⇒Portland, Oregon
5. 29°N latitude, 95°W longitude ⇒Houston, Texas
6. 43°N latitude, 79°W longitude ⇒Niagara Falls, New York
7. 25°N latitude, 80°W longitude ⇒ Miami, Florida
What is a longitude?The term Longitude has been refered as the horizontal lines that are the measurement east or west of the prime meridian. Longitude are the imaginary lines that divide the Earth. Longitudes are also called the meridians, which run from north to south pole to pole but they measure the distance east or west.
The hypothesis that the species diversity is greater at lower latitudes than higher latitudes because low-latitude habitats are older would be supported if speciation rates were: the same at high and low latitudes.
Species diversity can be defined as the number of species, present in an area or the ecosystem. More are the number of species, more diverse is the area is. The richness and functionality of an ecosystem is estimated through its diversity.
Therefore,longitudes are the horizontal lines which divide the Earth.
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What is a similarity between chemical change and chemical properties
Answer:
How are physical and chemical changes similar and different? (compare and contrast) (Physical and chemical changes are similar because matter experiences a change in state, Physical changes are different because matter remains the same substance, just in a different state, whereas chemical changes change the matter
draw the well labelled diagram of thermo flask.
Answer:
Here the answer is attached
Explanation:
An book fell from a shelf 1.5 meters from the ground. If it took the book 3 seconds to hit the ground, what was the velocity of the book?
The initial velocity of the book before its hits the ground is 14.2 m/s.
The given parameters;
height of the book above the ground, h = 1.5 mtime of motion of the book, t = 3 secondsThe initial velocity of the book is calculated as follows;
h = ut + ¹/₂gt²
where;
u is the velocity of the book1.5 = 3u + (0.5 x 9.8 x 3²)
1.5 = 3u + 44.1
3u = 1.5 - 44.1
3u = -42.6
[tex]u = \frac{-42.6}{3} \\\\u = -14.2 \ m/s\\\\u = 14.2 \ m/s \ downwards[/tex]
Thus, the initial velocity of the book before its hits the ground is 14.2 m/s.
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Why are occupants of the international space station weightless?
A jogger runs 12.0 blocks due east then 5.0 blocks due south. Find the magnitude of the joggers net displacement ?
Answer: 13.0 blocks
Explanation:
a football quarterback throws a football. after it leaves his hand, what forces are acting on the football? choose all that apply.
golekeeper
Explanation:
because they use hand to save keeper
How much must an object weigh to be able to float in water?
1: more than the amount of water it displaces
2: less than the amount of water it displaces
3: more than a gram
4: less than a gram
Answer:
less than one gram
Explanation:
big brain
Answer:
less than a gram
Explanation:
because yes
Sonar is a device that uses reflected sound waves to measure underwater depths. If a sonar signal has a frequency of 288 Hz and the speed of sound in water is 1450 m/s, what is the wavelength of the sonar signal?
A basketball is tossed upwards with a speed of 5.0 m/s. We can ignore air resistance. What is the maximum height reached by the basketball from its release point? (Answer using a coordinate system where upward is positive.)
Answer:
the maximum height is 1.276 meters
what is the prefix of 10^10
PLEASE BE FAST :)
If Runner A ran 1 mile in 7 minutes and Runner B ran 1 mile in 5 minutes, who ran at a faster speed.
Answer:
B
Explanation:
ran a mile 2 minutes faster
what is the central idea for stacking rocks vertically to test the effects of forces
Answer:
You can see how forces can stack on one another by comparing the normal force of the bottom most rock to the normal force of the upper most rock.
Explanation:
Say you have 3 rocks all with mass m=3kg
These 3 rocks will all have the gravitational force of -29.4N (multiply 3kg by -9.8m/s^2)
If none of the rocks are stacked, then they all have the same normal force as well (29.4N)
However, stack them, and see how their normal forces change.
m1 will continue to have a normal force of 29.4N
m2 will now have a normal force of 58.8
m3 will now have a normal force of 88.2
Though they all retain the same gravitational force, their normal force changes depending on the forces acting down on them.
Mass 1 have no forces acting downwards other than gravity.
Mass 2 has the force of mass 1 and gravity acting down on it.
Mass 3 has the force of mass 1, mass 2, and gravity acting down on it.
A box is pushed by a force of 15 N and accelerates 2 m/s2. What is the mass of the box?
Answer:
7.5 kgExplanation:
The mass of the box can be found by using the formula
[tex]m = \frac{f}{a} \\ [/tex]
f is the force
a is the acceleration
From the question we have
[tex]m = \frac{15}{2} = 7.5 \\ [/tex]
We have the final answer as
7.5 kgHope this helps you
How much work does a 60 Watt motor perform in 5 minutes?
Answer:
18000J or 18kJ
Explanation:
Use the formula:
work done or energy = power × time
power = 60Wtime = 5 mins = 300s (5 × 60)Sub in the values:
work done or energy = 60 × 300 = 18000Answer = 18000J or 18kJHope this helps!
if a person with the arm dimensions shown pushes down hard with a 90 n force, what force must the triceps muscle provide? ignore the mass of the arm and hand in your calculation.
Answer:
1125 N
Explanation:
what are the intermolecular forces present in water?
123456789 cari aja sendiri
Answer:
The main intermolecular forces present in water is hydrogen bond.
It is followed by,
Dipole-dipole attractions
Dipole-induced dipole attractions
London dispersion forces
The hydrogen bonds are the strongest force, but the other types of intermolecular attraction are still present.
At a race car driving event, a staff member notices that the skid marks left by the race car are
10.99 m long as it comes to a stop. The very experienced staff member knows that the
deceleration of a car when skidding is -42.61 m/s2. What can the staff member estimate for
the original speed of the race car if it came to a stop during the skid?
A car that experiences a deceleration of -41.62 m/s² and comes to a stop after 10.99 m has an initial velocity of 30.60 m/s.
A car experiences a deceleration (a) of -41.62 m/s² and comes to a stop (final velocity = v = 0 m/s) after 10.99 m (s).
We can calculate the initial velocity of the car (u) using the following kinematic equation.
[tex]v^{2} = u^{2} + 2as\\\\u = \sqrt[]{v^{2}-2as} = \sqrt[]{(0m/s)^{2}-2(-42.61m/s^{2} )(10.99m)} = 30.60m/s[/tex]
A car that experiences a deceleration of -41.62 m/s² and comes to a stop after 10.99 m has an initial velocity of 30.60 m/s.
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640 nanometer setara dengan
Answer:
640 nanometer setara dengan 6.4e-7 meter
please helpppp 12 points
which of the following is a selectively permeable membrane?
a) nulcer membrane
b) plasma membrane
c) cell wall
d)none of these
Answer:
B
Explanation:
The plasma membrane is a selectively premeable membrane that chooses what goes in and out of the cell. The cell wall is for support and the nuclear membrane decides what goes in and out of the nucleus
Answer:
Plasma membrane
Explanation:
The plasma membrane consists of a lipid bilayer that is semipermeable.The plasma membrane regulates the transport of materials entering and exiting the cell.So, it is selectively permeable membrane.
To make a solution for an experiment, Gunther needs to add 40 g of a solute to 100 g of water. When making the solution at room temperature, he could only add 34 grams before the solute settled out.
What could he do to dissolve the remaining 6 grams of the solute?
a) Put the solution in an ice bath, dissolve the solute, and let the solution return to room temperature.
b) Heat the solution, dissolve the solute, and let the solution cool verifying nothing settled out.
c) Add more water, boil the solution, and dissolve the solute until the some of the water evaporates.
d) Keep the solution at room temperature, add more water, and dissolve the excess solute.
Answer:
b.
Explanation:
b) Heat the solution, dissolve the solute, and let the solution cool verifying nothing settled out.
what is his angular displacement during a 1.0 s time interval?
Answer:
The angular velocity is: (2π radians) ⁄ (4.3 sec) = 1.461 rad/sec
The angular displacement is: (1.461 rad/sec)(1 sec) = 1.461 radians
Explanation: