Question

Idaho Jo is doing physics experiments throughout the solar system. She travels to each planet and shoots a potato straight up in the air with her potato gun. She uses the SAME POTATO ON EACH PLANET and THE INITIAL VELOCITY IS THE SAME EVERY TIME. She repeats the experiment on all 8 planets in the solar system.
Planet Free-fall Acceleration
Mercury 3.7 m/s2
Venus 8.9 m/s2
Earth 9.8 m/s2
Mars 3.6 m/s2
Jupiter 24.9 m/s2
Saturn 10.6 m/s2
Neptune 11.7 m/s2
Uranus 8.9 m/s2

On which planet(s) will the potato reach the highest altitude?


Mercury / Mars

Venus / Uranus

Earth

Jupiter

Answer 1

Answer:

Mercury / Mars

Explanation:

For an object launched straight upward, the following SUVAT equation can be used

$v^2-u^2=-2gh$

where

v is the final velocity

u is the initial velocity

g is the acceleration of gravity (free fall acceleration) (the negative sign is due to the downward direction of gravity)

h is the maximum height reached

At the maximum height, the velocity is zero, so v = 0. Re-arranging the equation,

$h=\frac{u^2}{2g}$

So we see that for equal initial velocity (u), the maximum height reaches is inversely proportional to the acceleration of gravity. Therefore, the potato gun will reach the highest altitude in the planets with lowest acceleration of gravity, therefore Mercury and Mars (3.7 and 3.6 m/s^2).