suppose you can jump to a height of 1.7 ft on earth (.52m). If you expand that same energy (do the same amount of non-conservative work) jumping on the moon, how high could you jump on the moon?

Answer 1

For this problem, we know that initially you were on the surface you were jumping off of (x=0) and you reached a height of 0.52m. We also know that when you reached that height, your velocity will be momentarily zero (v=0) and just as you leave the surface you will be moving at some positive velocity (v₀=?) On Earth, acceleration due to gravity would be -9.8m/s², so we can use the kinematic equation v² = v₀ + 2ax to find how fast you kicked off the ground.

0² = v₀² + 2 × -9.8m/s² × 0.52m

v₀² = 10.192m²/s²

v₀ = 3.2m/s

Now, you may be thinking that if you are lighter on the moon you would be able reach a higher initial velocity, and you would be technically correct. However, force is equal to mass times acceleration, not weight times acceleration. As a result, even though you don't weigh as much on the Moon, you still possess the same number of particles, and thus mass, as you do on Earth, and it will take the same amount to move them as before. Now, the lower force on you would probably mean that the net force on you is decreasing, allowing you to accelerate more as you jump, but finding out how this changes would require knowing things like your mass, how long it takes you to go from your lowest crouch to lifting off, and all sorts of other variables that would make this problem much more complicated than it has to be. TLDR, we shall just assume v₀ is still 3.2m/s on the Moon.

Acceleration on the Moon is only -1.625m/s² and velocity at the height of your jump will still be zero. Let's plug in the new numbers, this time with x as the unknown.

0 = (3.2m/s)² + 2 × -1.625m/s² × x

0 = 10.192m²/s² - 3.25m/s² × x

x = 3.1m

So you should be able to jump 3.1 meters, or about 10.2 feet.