You can jump to a height of 2.6625 ft (0.81153 m) on Earth. If you expend the same energy jumping on the moon where the acceleration of gravity is only 1.6 m/s2, how high would you rise?

Answer 1

On earth, the energy you have when you reach the top of your flight is potential energy defined as "mgh" where "m" is your mass, "g" is the acceleration due to gravity on earth and is 9.81 m/s² and h = 0.81153 meters

So mgh = m(9.81)(0.81153) = 7.9611m

On the moon, you also want to expend the same amount of energy or 7.9611m so:

7.9611m = mgh where "m" is your mass, "g" is the acceleration due to gravity on the moon and is given as 1.6 m/s² so:

7.9611m = m(1.6)h

Dividing both sides by "m":

7.9611 = 1.6h

h = 5.0 meters (you are given the acceleration due to gravity on the moon in 2 sig figs so we round to 2 sig figs)