Question

A grapefruit falls from a tree and hits the ground 0.72 s later.

How far did the grapefruit drop?
What was its speed when it hit the ground?

Answer 1

The grapefruit dropped 2.54 m and hit the ground at 7.06 m/s

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)`

Given a grapefruit free falls from a tree and hits the ground t=0.72 s later, we can calculate the height it fell from:

`\displaystyle y=(9.8\cdot 0.72^2)/(2)`

y = 2.54 m

The final speed is computed below:

`vf=9.8\cdot 0.72`

vf = 7.06 m/s

The grapefruit dropped 2.54 m and hit the ground at 7.06 m/s