(7%) Problem 13: Gravitational acceleration on the moon is one sixth of that on

Question

(7%) Problem 13: Gravitational acceleration on the moon is one sixth of that on Earth A ball released from rest above the surface falls from height d in a time of t-0.75 seconds ©theexpertta.com 25% Part (a) Write an expression for the final velocity vf of the ball when it impacts the surface of the moon assuming it is dropped from rest. This expression should be in terms of only, g (the gravitational acceleration on Earth), and time, . -a 25% Part (b) Calculate the final velocity, vf, numerically in m/s. 25% Part (c) Calculate the height, d (in meters), from which the ball was dropped. D A it did on the moon? 25% Part (d) From how high up would this ball need to be dropped on the earth, de (in meters), if it took the same time to reach the ground as Grade Summary Deductions 100% Potential de 0%

Explanation / Answer

a)from eqn of motion

v = u + at

u = 0 as it had been dropped from rest ; a = g ;

In terms of g and t

vf = 0 + g t

Hence, vf = g t

b)vf = g t

g = 9.81/6 = 1.635 m/s^2

vf = 1.635 x 0.75 = 1.226 m/s

Hence, vf = 1.226 m/s

c)we know that

s = ut + 1/2 at^2

h = 0 + 0.5 x 1.635 x 0.75^2 = 0.46 m

Hence, h = 0.46 m

d)On earth, g = 9.81 m/s^2

d = 0 + 0.5 x 9.81 x 0.75^2 = 2.76 m

Hence, d = 2.76 m

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