Question

Astronauts on our moon must function with an acceleration due to gravity of 0.170. How much longer would it be in motion (going up and coming down) on the moon than on earth?

Answer 1

first, I think you have got your figure wrong. Gravity on the moon is more like 1.6m/ss, ie a sixth, not a sixtieth, of the earth's!

if you put the same amount of energy into a jump, on the moon you should rise 6 times as high. that's calculated simply by comparing the end potential (gravitational) energy you would have acquired - mgh. and assuming no energy losses.

for a jump of 1 metre on earth, the jump h on the moon is given as:

mass * 1.6 * h = mass * 9.8 * 1

mass cancels giving h ~ 6m.

by the same token you would be in motion longer on the moon by a factor of x6.

the time t before you reach the peak of a jump or bounce is given by t = u/a where a is the start velocity, simply put the vertical speed at which you leave the surface.

this start velocity will be the same for jumps taking the same amount of every - seen simply by comparing the formula for kinetic energy KE = 1/2mv^2. ie the kinetic energy you acquire is irrespective of gravity.

comaparing times gives the same result, you will spend 6x more time off the ground on the moon.