A man can jump 1.5 m on earth. Calculate the approximate height he might be able to jump on a planet whose density is one quarter
of the earth and where radius is one third that of the earth.

Mass = volume x density. Volume(2) = 1/3, density is 1/4, so

Mass = 1/3 * 1/4 = 1/12 that of Earth.

Surface gravity = m /r^2 = 1/12 / (1/4)^2 = 1/12 / 1/16 = 16/12 = 4/3 Earth’s

So… surface gravity would by 13 m/s^2 vs. 9.8m/s^2

Someone able to jump up 1.5m vs. 9.8m/s^2 is imparting 5.4 m/s of velocity on themselves. Imparting 5.4m/s of velocity on yourself against 13m/s^2 gravity, you would reach 0 velocity at:

1.12m in height.