Answer:
The magnitude of the acceleration due to gravity is [tex]5\ m/s^2[/tex]
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:
[tex]\displaystyle y=\frac{gt^2}{2}[/tex]
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:
[tex]\displaystyle g=\frac{2y}{t^2}[/tex]
The astronaut drops an object from rest and observes when t=2 seconds, y=10 m, thus:
[tex]\displaystyle g=\frac{2\cdot 10}{2^2}=\frac{20}{4}[/tex]
[tex]g=5\ m/s^2[/tex]
The magnitude of the acceleration due to gravity is [tex]\mathbf{5\ m/s^2}[/tex]
