Need help with physics problem

Question

The tallest volcano in the solar system is the 29 km tall Martian volcano, Olympus Mons. An astronaut drops a ball off the rim of the crater and that the free fall acceleration of the ball remains constant throughout the ball’s 29 km fall at a value of 3 m/s 2 . (We assume that the crater is as deep as the volcano is tall, which is not usually the case in nature.) Find the time for the ball to reach the crater floor. Answer in units of s.

Answer 1

This is a kinematics in one direction problem. Since we know the distance (29 km), the acceleration (3 m/s²), and the initial velocity (0, since it's being dropped), we can use the following equation to find time:

d = v_it + ¹/₂ at²

We have to convert km to m so that are units are consistent, so instead of 29 km we use 29000 m.

Setting our zero point as the top of the volcano and downward as the negative direction,

-29000 = 0 + ¹/₂ (-3) t²

-29000 = -1.5 t²

19,333.33 = t²

139 s = t

So it takes 139 seconds to hit the bottom.