Zero, a hypothetical planet, has a mass of 5.5 x 1023 kg, a radius of 2.8 x 10° m, and no atmosphere. A 10 kg space probe is to belaunched vertically from its surface. (a) If the probe is launched with an initial kinetic energy of 5.0 x 107 J, what will be its kineticenergy when it is 4.0 x 106 m from the center of Zero? (b) If the probe is to achieve a maximum distance of 8.0 x 106 m from the centerof Zero, with what initial kinetic energy must it be launched from the surface of Zero?(a) Number:iUnits:(b)Number:iUnits:

Name: Zero, a hypothetical planet, has a mass of 5.5 x 1023 kg, a radius of
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Description: Zero, a hypothetical planet, has a mass of 5.5 x 1023 kg, a radius of 2.8 x 10° m, and no atmosphere. A 10 kg space probe is to belaunched vertically from its surface. (a) If the probe is launched with an initial kinetic energy of 5.0 x 107 J, what

Given:- A hypothetical planet has a mass of M = 5.5 x 1023 kg, a radius of Ri = 2.8 x 106 m, and no atmosphere. A m = 10 kg space probe is to be launched vertically from its surface. Find:- (a) If the probe is launched with an initial kinetic energy of 5.0 x 107 J, what will be energy when it is Rf = 4.0 x 106 m from the center of Zero? (b) If the probe is to achieve a maximum distance of Rf = 8.0 x 106 m from the center of Zero, with what initial kinetic energy must it be launched from the surface of Zero?Solution:- a) We know that The gravitational Force is conservation force, The mechanical energy of the probe planet system is conserved Ei= EfKi -GMmRi = Kf- GMmRiKf= Ki - GMm1Ri-1RfKf = 5.0×107 - 6.67×10-11×5.5×1023×1012.8×106-14.0×106Kf = 10694642.86 = 1.0694×107 J Kf= 1.0694×107 J The final kinetic energy is 1.0694 x 107 J b) Now at the maximum height, The speed of the probe will be Zero then By the law of the conservation of the energy is given as Ei= EfKi - GMmRi = Kf - GMmRf Ki = Kf - GMm1Rf-1RiKi=0 - GMm1Rf-1RiKi= - GMm1Rf-1RiKi= - 6.67×10-11×5.5×1023×1018.0×106-12.8×106Ki= 8.516×107 J The initial kinetic energy must it be launched from the surface of Zero is 8.516 x 107 J

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Zero, a hypothetical planet, has a mass of 5.5 x 1023 kg, a radius of 2.8 x 106 m, and no atmosphere aunched vertically from its surface. (a) If the probe is launched with an initial kinetic energy of 5.0 energy when it is 4.0 x 106 m from the center of Zero? (b) If the probe is to achieve a maximum dist

Zero, a hypothetical planet, has a mass of 5.5 x 1023 kg, a radius of 2.8 x 106 m, and no atmosphere aunched vertically from its surface. (a) If the probe is launched with an initial kinetic energy of 5.0 energy when it is 4.0 x 106 m from the center of Zero? (b) If the probe is to achieve a maximum dist

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ISBN:9781305952300

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Chapter1: Units, Trigonometry. And Vectors

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Simple harmonic motion

Simple harmonic motion is a type of periodic motion in which an object undergoes oscillatory motion. The restoring force exerted by the object exhibiting SHM is proportional to the displacement from the equilibrium position. The force is directed towards the mean position. We see many examples of SHM around us, common ones are the motion of a pendulum, spring and vibration of strings in musical instruments, and so on.

Simple Pendulum

A simple pendulum comprises a heavy mass (called bob) attached to one end of the weightless and flexible string.

Oscillation

In Physics, oscillation means a repetitive motion that happens in a variation with respect to time. There is usually a central value, where the object would be at rest. Additionally, there are two or more positions between which the repetitive motion takes place. In mathematics, oscillations can also be described as vibrations. The most common examples of oscillation that is seen in daily lives include the alternating current (AC) or the motion of a moving pendulum.

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Question

Zero, a hypothetical planet, has a mass of 5.5 x 1023 kg, a radius of 2.8 x 10° m, and no atmosphere. A 10 kg space probe is to be
launched vertically from its surface. (a) If the probe is launched with an initial kinetic energy of 5.0 x 107 J, what will be its kinetic
energy when it is 4.0 x 106 m from the center of Zero? (b) If the probe is to achieve a maximum distance of 8.0 x 106 m from the center
of Zero, with what initial kinetic energy must it be launched from the surface of Zero?
(a) Number:
i
Units:
(b)
Number:
i
Units:

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