10. a scientist throws a rock straight upwards on mars and
it reaches a height of 55m.
a. what was the initial velocity of the rock?
| b. how long was the rock in the air for?

a. 20.4 m/s upward

The motion of the rock thrown upward is a free-fall motion, with a constant acceleration downward, given by

(acceleration of gravity on Mars)

So, we can use the following suvat equation:

where

v is the final velocity  of the rock

u is the initial velocity

a is the acceleration  ()

s is the displacement

For the rock in the problem:

v = 0 (at the maximum height, the velocity is zero)

s = 55 m (the maximum height)

Solving for u, we find the initial velocity:

b. 10.74 s

First of all, we can find the time the rock takes to reach the maximum height, that is given by the equation

And solving for t,

Now we notice that the motion of the rock is symmetrical, so the way down takes exactly the same as the way up: therefore, the total time of flight of the rock is