Astronauts on our moon must function with an acceleration due to gravity of 0.16

Question

Astronauts on our moon must function with an acceleration due to gravity of 0.165g .

Part A If an astronaut can throw a certain wrench 15.0 m vertically upward on earth, how high could he throw it on our moon if he gives it the same starting speed in both places?

Part B How much longer would it be in motion (going up and coming down) on the moon than on earth?

Please explain in detail how you approached each step. There are a lot of similar questions like this on Chegg but they're all very unclear on how to approach it. I want to learn to do it on my own. I don't want the answer only. Thanks

Explanation / Answer

we assume upward direction is positive

gravity at moon = gm =0.165g = 0.165 * 9.8 = 1.617 m/s^2

at maximum height final velocity is equal to zero he thorw wrench 15 m at earth

v^2 = u^2 + 2as

s = hmax = 15 m

0 = u^2 - 2*9.8*15

u = sqrt(2*9.8*15)

u = 17.146 m/s

now he throw at moon

v^2 = u^2 - 2gm*hmax

at maximum height v = 0

hmax = u^2/2*gm

hmax = 90.9 m

part b)

s = ut + 1/2at^2

since displacement is zero ( wrench is returning to ground back)

0 = ut + 1/2at^2

t = -2u/a

a = at eatth = g = -9.8 m/s^2

t = -2*17.146/9.8 = 3.499s = 3.5 s

time at moon

t = -2*17.146/1.617 = 21.2 s

wrench will be in motion 17.7 s longer at moon

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