Falling Down

Classical Mechanics Level 1

You jump off a building of arbitrary height into a pool of water. Would your speed when you hit the water be higher if you were on the moon, or if you were on the earth?

On the Earth On the Moon

1 solution

Oliver Papillo
Dec 23, 2017

Instead of the moon and the earth, suppose we have two planets, with different constant accelerations, where planet 1 has a higher mass (and therefore constant acceleration) than planet 2.

Acceleration of planet $1 = a$

Acceleration of planet $2 = b$

Fall height $= c$

Distance covered (for time $t$ ) on planet $1 = \frac{at^2}{2} = c$

Distance covered (for time $t$ ) on planet $2 = \frac{bt^2}{2} = c$

Time taken on planet $1 = \sqrt{2c/a}$

Time taken on planet $2 = \sqrt{2b/a}$

Speed at impact on planet $1 = a \sqrt{2c/a} = \sqrt{2ac}$

Speed at impact on planet $2 = b \sqrt{2c/b} = \sqrt{2bc}$

As $a>b>0$ , $\sqrt{a} > \sqrt{b}$ , you hit the ground faster on the larger (mass-wise) planet, so you hit the water faster on the Earth .

Falling Down

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