Question

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?

Answer 1

The magnitude of the acceleration due to gravity is
`5\ m/s^2`

Step-by-step 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:

`\displaystyle y=(gt^2)/(2)`

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:

`\displaystyle g=(2y)/(t^2)`

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

`\displaystyle g=(2\cdot 10)/(2^2)=(20)/(4)`

`g=5\ m/s^2`

The magnitude of the acceleration due to gravity is
`\mathbf{5\ m/s^2}`