Question

An astronaut on a distant planet wants to determine its acceleration due to gravity. The astronaut throws a rock straight up with a velocity of +15 m/s and measures a time of 20.0 s before the rock returns to his hand. What is the acceleration (magnitude and direction) due to gravity on this planet?

Answer 1

A diagram of the path of the rock is shown in Fig. 2.6. The y axis is measured upward from the position of the hand. We know the initial velocity of the rock, v₀ = +15.0 m/s but we don’t know the value of the acceleration, ay. (We do know that it will be a negative number, because objects fall down on this planet too!) We know that at t = 0.0 s y is 0.0 m (of course) but we also know that at t = 20.0 s, y is equal to 0.0 s.

from which we can find a. Some algebra gives us:

The magnitude of the acceleration due to gravity on the planet is 1.50 m/s² and from the minus sign we know that the direction of the acceleration is downward. (No surprise... things fall down on other planets as well!