On an unknown planet, an astronaut drops an object from rest. She observes that the object falls a distance of 10 meters during a time interval of 2 seconds. What is the magnitude of the acceleration due to gravity on that planet?

The magnitude of the acceleration due to gravity is  

Explanation:

Free Fall Motion

A free-falling object falls under the sole influence of gravity of the planet and do not encounter air resistance.

If an object is dropped from rest in a free-falling motion, it falls with a constant acceleration called the acceleration of gravity, which value depends on the planet where the motion occurs.

The distance traveled by a dropped object is:

Where t is the time taken to fall a distance y and g is the acceleration of gravity. If we know t and y, then we can calculate the value of g by solving the above equation for g:

The astronaut drops an object from rest and observes when t=2 seconds, y=10 m, thus:

The magnitude of the acceleration due to gravity is