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

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

Step-by-step 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=(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{(2h)/(g)}`

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

`\displaystyle t=\sqrt{(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