Question

A ball is dropped from a treetop 64 feet above the ground. How long does it take to hit the ground? (s = 16t 2)

1 second
2 seconds
3 seconds

Answer 1

Option 2nd is correct

2 seconds does it take to hit the ground

Explanation:

The equation of projection is given by:

`s(t) = -at^2+v_ot+h`

where,

`a \approx -16 m/s^2`

`v_0` is the initial velocity

and h is the initial height.

As per the statement:

A ball is dropped from a treetop 64 feet above the ground.

Initial height: s(0) = 64 feet

Since, initial velocity
`v_0 = 0`

then equation becomes:

`s(t) =-16t^2+0t+64`

To find the how long does it take to hit the ground.

Substitute s(t) = 0 then ;

`0 =-16t^2+0t+64`

⇒
`0 = -16t^2+64`

⇒
`16t^2= 64`

Divide both sides by 16 we have;

`t^2 = 4`

Simplify:

`t =\pm √(4) =\pm 2`

Since, t is the time cannot be in negative

⇒t = 2 seconds

Therefore, 2 seconds does it take to hit the ground.

Answer 2

It takes 2 seconds long to hit the ground. The correct answer between all the choices given is the second choice. I am hoping that this answer has satisfied your query and it will be able to help you in your endeavor, and if you would like, feel free to ask another question.