What is the power rating of an engine capable of lifting a 100 kg object 5 m vertically in 4 seconds? do not include units in your answer.

1. The equation of trajectory is: y = 5x²/4 +2x; it is equation of parabola.

2. The  position vector = 2ti + (5t² +4t) j

3. The position of point M at t = 3 s is: ( 6,57).

4. The magnitude of velocity of point M at any time t is 2√(25t²+20t+5).

5. The magnitude of acceleration is 10m/s².

The rate at which a body's displacement changes in relation to time is known as its velocity. Velocity is a vector quantity with both magnitude and direction. SI unit of velocity is meter/second.

coordinates at any instant t are:

x = 2t; y = 5t² +4t

1. equation of trajectory is:

y = 5x²/4 +2x; it is equation of parabola.

2. position vector = 2ti + (5t² +4t) j

3.  the position of point M at t = 3 s is: x = 2×3 = 6; y = 5×3² +4×3 = 57; i.e., ( 6,57)

4.  the velocity vector of point M at any time t is = 2i + ( 10t +4) j

magnitude of velocity = √( 2² + (10t +4)² = 2√(25t²+20t+5).

5.  the acceleration vector is = 10j m/s²

Hence, its magnitude is =10m/s².

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Due to the uniform distribution of leaves, folivores rarely exhibit dominance hierarchies.

A dominance hierarchy is a type of social hierarchy that arises when members of a social group interact, to create a ranking system. In social living groups, members are likely to compete for access to limited resources and mating opportunities. Rather than fighting each time they meet, relative rank is established between members of the same se x. Based on repetitive interactions a social order is created that is subject to change each time a dominant animal is challenged by a subordinate one. This hierarchical structure can be observed in many species, including humans.

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The slope of a line is a measure of the steepness of its angle with the x-axis. A line parallel to the x-axis has no angle and therefore has a slope of 0.

The slope of a line is a measure of the steepness of its angle with the x-axis. It is calculated by taking the ratio of the change in y-coordinates to the change in x-coordinates (rise over run). A line parallel to the x-axis has no angle and therefore has no rise or run. This means that the change in y-coordinates over the change in x-coordinates is 0, resulting in a slope of 0. This is true for any line parallel to the x-axis, regardless of its length or orientation. A line perpendicular to the x-axis will have a slope of either positive or negative infinity, depending on its orientation. A line that is neither parallel nor perpendicular to the x-axis will have a slope greater than 0 but less than infinity, depending on its angle with the x-axis.

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Explanation:

4.08 seconds thank me later

(a) The fraction of neutron's kinetic energy transferred to the atomic nucleus is 0.088.

(b) The final kinetic energy of the neutron is  4.95 x 10⁻¹³ J.

The final velocity of the atom is calculated by applying the principle of conservation of linear momentum as follows;

initial momentum of the neutron = final momentum of the atom

m₁u₁  = m₂u₂

where;

The mass of the atomic nucleus = 11.4 m₁

u₂  = m₁u₁ / m₂

u₂  = m₁u₁ / (11.4 m₁)

u₂  = 0.088u₁

The initial kinetic energy of the neutron is calculated as;

K.Ei = ¹/₂m₁u₁²

The final kinetic energy of the atomic nucleus is calculated as;

K.Ef =  ¹/₂m₂u₂²

K.Ef =  ¹/₂(11.4 m₁)(0.088u₁)²

K.Ef = 0.088 (¹/₂m₁u₁²)

K.Ef = 0.088 (K.Ei)

The fraction of neutron's kinetic energy transferred to the atomic nucleus is calculated as;

= 0.088 (K.Ei) / K.Ei

= 0.088

= 8.8 %

The final kinetic energy of the neutron is calculated as follows;

K.E.f (neutron) = (1 - 0.088) x (5.43 x 10⁻¹³ J)

K.E.f (neutron) = 4.95 x 10⁻¹³ J

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the internal enclosure wall is 539 K degrees in temperature. If a container has a 50 m2 interior space, the interior surface is black, and the container is kept at a constant temperature,

The answer solely depends on how well-insulated your house is. If your property is very well insulated, it is best to leave the heating on at a preset temperature, where thermostat and boiler can easily maintain the temperature because there is little heat loss.

Ohm's law states that temperature will remain constant, hence [heat] = vIt, where t is a constant. Since v and I are directly proportional, increasing v will likewise increase I, increasing v will result in an increase in heat (temperature).

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The gravitational force exerted on the moon while it is in orbit around the planet is 1 × 10¹⁹ N.

Gravitational Field Strength is defined as the gravitational force per unit mass experienced by a point mass at a certain point.  It is  a vector quantity having SI unit Newton/kg.

Mass of the moon: M = 1 ×10²² kg.

The gravitational field strength at a distance r from the planet is: E= 0.001 N/kg.

Hence, gravitational force acting on the moon: F = mE

= 1 ×10²² × 0.001 N

= 1 × 10¹⁹ N.

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The water based transport is called a ship when it weighs more than 500 tonnes.

The differences between boat and ship are stated for detailed clarification on the two-

Concerning size, ship is larger than a boat. It can be understood from the fact that boat can be shipped in a ship but ship can not be transported in a boat.

Boats are used in small areas and smaller purposes. Ships are used in seas and oceans for cargo and passenger transport.

Subsequently, based on large size and large medium of transport, the crew members in shop are more than boat. They include engineers, navigators, technicians and other important individuals.

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The S.I unit of wavelength is metre. The wavelength is the separation between two crests or troughs that occur back-to-back.

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The highlighted vessel  given below in the image attached:

What is the function of the coronary arteries and cardiac veins?

The movement of blood through the blood arteries that nourish the heart muscle is known as coronary circulation (myocardium). The heart muscle receives oxygenated blood from the coronary arteries. After the blood has been deoxygenated, cardiac veins remove it.

The heart muscle receives blood from coronary arteries. The heart muscle need oxygen-rich blood in order to operate, just like all other bodily components do. Blood that lacks oxygen must also be transported away. Outside of the heart, the coronary arteries encircle the organ.

Therefore, Your heart receives blood through the coronary arteries and their branches. In order to pump blood through your heart and the rest of your body, your heart muscles require the oxygen and nutrients found in blood.

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The frequency would have units of cycles/second, waves/second or vibrations/second.

Frequency, in physics, is the number of waves that pass fixed point in unit time; also, the number of cycles or vibrations undergone during one unit of time by a body in periodic motion.

What is frequency?

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Q=ne will be the formula used to determine the number of electrons. More details The quantity of energy or electrons that are transferred from one body to another by a variety of modes, such as conduction, induction, etc., is known as an electric charge.

A negatively charged subatomic particle known as an electron can either be free or attached to an atom (not bound). One of the three main types of particles within an atom is an electron that is bonded to it; the other two are protons and neutrons. The nucleus of an atom is made up of electrons, protons, and neutrons together.

By exchanging electrons to form chemical bonds, atoms join together to form molecules and compounds. Knowing the number of electrons attached to each atom is the first step in comprehending the nature of this bonding. You may determine the amount of electrons in a substance based on its chemical formula using information from a periodic chart of the elements and some simple math.

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The frequency of vibration of a string is given by f=2LnmT, where T is tension in the string, L is the length, n is the number of harmonics.

What is a frequencyy?

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Yes, Ballistic stretching can be harmful if it is not performed properly.

This type of stretching involves bouncing movements, which can place excessive strain on the muscles and connective tissues. This can lead to muscle strains or tears, as well as other injuries. It is important to use caution when performing ballistic stretches and to stop if any pain or discomfort is experienced. It is also recommended to warm up before stretching and to stretch slowly and smoothly, rather than using ballistic movements.

Ballistic stretching can also increase the risk of muscle imbalances and poor posture if it is not balanced with other types of stretching, such as static stretching. It is generally more effective and safer to gradually increase flexibility through regular, consistent stretching rather than trying to force the body to stretch too quickly or aggressively.

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Answer:

Total energy (E) =me=m(u+ke+pe)=U+KE+PE

The match description of these stars with their life cycle stage are as follows:

Stars follow the same 7-stage cycle in their lives. The life cycle is as follows:

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In gm two-mode hybrid electric vehicle, the vehicle can be powered by electric power alone in the first mode. The first mode has a function like a regular full hybrid.

A two-mode vehicle is a hybrid model that functions in two ways. The first mode is fully hybrid. The second mode brings a difference. The second mode performs various functions by adjusting various amounts of engine and motor functions.

In the first mode, with a light load and at low speed, the engine can be powered alone on electric power. In this mode, the engine can be shut down, but all accessories can continue operating on electric power. The hybrid system can restart the engine at any time when required.

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The 4 reasons why tariff are imposed are:

What is a Tariff?

A tariff is a type of tax levied on imported goods or services. Tariffs are a common element of international trade The main reasons for imposing tariffs include reducing imports of goods and services by raising prices and protecting domestic producers.

Customs duties usually take one of two forms: specific or ad valorem. A specific tariff is charged on a per-item basis (for example, a tariff of $1,000 per imported vehicle). An ad valorem tax is a duty charged as a percentage of the value of goods (eg 10% of the value of an imported car).

The 4 reasons why tariff are imposed are:

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Calcium is released by the action of osteoclasts which break down bone matrix.

The cells known as osteoclasts are responsible for breaking down bone to start the process of normal bone remodeling and for mediating bone loss in pathologic situations by escalating their resorptive activity. They develop in the bone marrow from progenitors in the myeloid/monocyte lineage, which then circulate in the blood. The Howship lacunae, which osteoclasts occupy on the surface of the bone, are assumed to be the result of the osteoclasts' enzymes eroding the bone. The union of many cells produced from blood-circulating monocytes results in osteoclasts. These are derived from the bone marrow in turn.

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Sonar, or underwater sound projectors, were originally utilised during World War I and were the first modern innovation in seafloor mapping.

Who was the first to map the ocean floor?

Sonar was being used to map deep water areas by the Coast and Geodetic Survey, which was the forerunner of NOAA's Ocean Service, by the 1920s.

Marie Tharp , who was born in Michigan in 1920, worked as both a geologist and a cartographer. Tharp was the first to map the ocean floor scientifically in collaboration with her coworker Bruce Heezen. In the 1940s, Tharp started her career in science as a geologist for Stanolind Oil. 

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The Philosophize Naturalis Principia Mathematica by Isaac Newton (1687) is the first work to explicitly state the cosmological principle.

Newton envisioned the Earth as a sphere in orbital motion around the Sun within an empty space that extended equally in all directions to impossibly enormous distances, in contrast to preceding classical or mediaeval cosmologies that saw the Earth as resting at the center of the universe.

The formal definition of the cosmological principle is "Viewed on a sufficiently wide scale, the properties of the cosmos are the same for all observers". This amounts to the firmly philosophical assertion that the cosmos as a whole, and not just the bit we can see, is governed by the same physical rules. In essence, this implies that the universe can be understood and is on scientists' side.

The cosmological principle has two testable consequences, an implicit qualification, and depends on a definition of "observer."

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A ball is attached to a string that is whirled around in a horizontal circle having the radius of r. If the radius of the circle is changed to r/4 and the same centripetal force is applied by the string, the new speed of the ball is one-half the original speed.

The formula for the centripetal force is

                 F = mv² / r

where F is the centripetal force

          m is the mass of the ball

          v is the velocity of the ball

          r is the radius of the circular movement

Let us rearrange the equation,

               [tex]\displaystyle v = \sqrt{\frac{Fr}{m}[/tex]

If the radius of the circular movement is reduced as r/4, then the velocity becomes,

               [tex]\displaystyle v = \sqrt{\frac{Fr}{4m}[/tex]

              [tex]\displaystyle v = \frac{1}{2} \sqrt{\frac{Fr}{m}[/tex]

which means that if the radius is reduced by one of forth the original, then the velocity will be reduced by twice the original.

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The complete question is

A ball attached to a string is whirled around in a horizontal circle having a radius of r. If the radius of the circle is changed to r/4 and the same centripetal force is applied by the string, the new speed of the ball is which of the following?

 (A) One-quarter the original speed

 (B) One-half the original speed  

(C) The same as the original speed

(D) Twice the original speed

(E) Four times the original speed

In the field of physics, total internal reflection refers to the entire reflection of a beam of light that is traveling through a medium such as water or glass back into the medium itself from the surfaces that surround the medium.

When the angle of incidence is larger than a specific limiting angle, which is referred to as the critical angle, the phenomena will take place. When a ray of light traveling through a medium with a higher index of refraction approaches another medium with an angle of incidence that is greater than the critical angle, a phenomenon known as total internal reflection occurs. In general, this phenomenon takes place at the boundary between two transparent media.

True statements are;

1. A smaller critical angle means the total internal reflection is more likely to occur.

2. Fiber optic cables are practical applications of total internal reflections.

False statements are;

1. When light hits a boundary at a less than the critical angle, it will undergo total internal reflection.

2. Single reflection of light of a silvered mirror is more efficient than total internal reflection so mirrors are often used instead of prisms in optical instruments to minimize light loss.

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This cart's speed at point 2 is indicated as √5GR

How fast is it?

This is how far something moves over a predefined or fixed length of time. Although it is the fastest, the for loop is difficult to read. The for each is quick, and iteration may be managed.

gravitational speed, or g.

m = the cart's mass

r = radius

1 speed equals v1.

f1 is  centripetal force

f1 = mv1²/R

m1 = mg

mv1²/R = mg

the cross-multiply v1² = gr

v1 = √gr

H = 2R

mgH x mv12/2 mv22/2

2GH + v1² = v2²

2g(2R) + (√gR)² = v2²

4gr + GR = V2²

5GR = v2²

√5GR = v2

As a result, at point 2, the cart's speed is indicated as √5GR

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The question is incomplete I can answered it in general way .

The equivalent emf of the collection will be 15.6 V. A conventional (i.e., non-quantum) field created by moving electric charges is known as an electromagnetic field (sometimes referred to as an EM field or EMF). It is the field that is described by classical electrodynamics (a classical field theory), and it is the classical analogue of the quantum electrodynamics' quantized electromagnetic field tensor (a quantum field theory).

The collection's equivalent emf can be obtained as shown below. The results of the investigation were as follows:

Emf 1 (E₁) = 3.0 V

Emf 2 (E₂) = 4.5 V

Emf 3 (E₃) = 1.5 V

Emf 4 (E₄) = 2.0 V

Emf 5 (E₅) = B₁ = 4.6 V

Equivalent emf (E) = ?

E = E₁ + E₂ + E₃ + E₄ + E₅

E = 3 + 4.5 + 1.5 + 2 + 4.6

E = 15.6 V

Therefore, the equivalent emf would be 15.6 V.

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Saturn planet has an orbital eccentricity most like the orbital eccentricity of the Moon.

An ellipse's eccentricity (e) is a value that affects how it looks, such as whether it is more rounded or if it resembles a segment. Let "a" be the major semi-axis and "c" be the focal semi-distance:

e = c / a

The gravitational forces that propel the planets disappear as they gracefully glide into an orbit around the Sun. However, a planet must follow an orbit to stay inside the bounds of the gravitational pull of other celestial bodies, particularly the sun.

The orbits have an ascending node, a vernal point, an argument of the perihelion, an eccentricity, an inclination, and an aphelion. The planets' orbits are all roughly on the same plane. The ecliptic is the name of this orbital plane.

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A simple compound microscope provides large magnification by employing a short focal length objective and a short focal length eyepiece.

A compound microscope is a high magnification microscope that uses two lenses to compound the level of magnification. The first lens is an objective lens and the second lens is an eyepiece lens.

In compound microscope both lenses are convex lenses. The objective lens has a very short focal length and hence has very high magnifying power (P ∝ 1/f ).

The image formed by the objective lens serves as the object to the eyepiece. The position of the eyepiece is kept such that the image formed by the objective lens is formed within the focal length of the eyepiece.

So, the focal length is short for eyepiece lens also.

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a word portion that is added to a root word to alter or modify its meaning; prefixes and suffixes are also considered affixes. combining vowel, word root, suffix, prefix, and suffix.

A root word is a word that has no prefixes or suffixes (a prefix is a string of letters that go at the start of a word; a suffix is a string of letters that go at the end of a word). We can alter the meaning of a root word by adding prefixes and suffixes. For instance, the suffixly is added to the word love to create the word beautiful. While a root can serve as the foundation for a new term, it rarely does so.

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The formula for calculating lambda is: Lambda = (E1 – E2) / E1.

Lambda is the symbol for wavelength it isn't a constant there for no standard value

it is linked to frequency:

frequency x Wavelength = speed of light (3x10^8)

What is lambda?

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Answer:

Hence, the isotope will take about 6.645T years to reduce to 1% of its original value