Question

A package is dropped from the height of 100 m and falls freely. How fast will the package be traveling when it hits the ground?

Answer 1

Answer:

The package will be traveling at 44.3 m/s when it hits the ground

Explanation:

Free Fall Motion

A free-falling object falls under the sole influence of gravity. Any object that is being acted upon only by the force of gravity is said to be in a state of free fall. Free-falling objects 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 is $g = 9.8 m/s^2$.

The final velocity of a free-falling object after a time t is given by:

vf=g.t

The distance traveled by a dropped object is:

$\displaystyle y=\frac{gt^2}{2}$

If we know the height h from which the object was dropped, we can find the time it takes fo hit the ground:

$\displaystyle t=\sqrt{\frac{2h}{g}}$

The package was dropped from h=100 m, thus the time taken to reach the ground is:

$\displaystyle t=\sqrt{\frac{2(100)}{9.8}}$

$t = 4.52~s$

The final speed is now calculated:

$vf=9.8*4.52$

$vf=44.3~m/s$

The package will be traveling at 44.3 m/s when it hits the ground