Question

A penny is dropped from the 82nd Floor Observatory of the Empire State Building. The penny will fall for 8.1s before hitting the ground. 1. How far does the penny fall? 2. How fast is the penny going when it hits the ground?

Answer 1

vf=79.38 m/s

y= 321.5 m

Step-by-step explanation:

Free Fall Motion

A free-falling object falls under the exclusive influence of gravity. 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)`

1.

The penny will fall for t=8.1 s before hitting the ground, thus the height from which it was dropped is:

`\displaystyle y=(9.8\cdot 8.1^2)/(2)`

y= 321.5 m

2.

The final velocity is:

`vf=9.8\cdot 8.1`

vf=79.38 m/s