Question

A ball is dropped from a height of 64 feet. Its height, in feet, can be modeled by the function h(t) = -167 + 64, where t is the time in seconds since it is dropped.

(a) Find how long it takes the ball to reach the ground.
(b) Find how long it takes the ball to fall 36 feet. (Hint: first find its
height.)

Answer 1

Explanation:

Known facts:

• the ball dropped from a height of 64 feet
• function
  `h(t) = -16t^(2) + 64`

First question:

• the ball hits the ground when h(t) = 0, thus we get the equation

`-16t^(2) +64 = 0\\16t^(2) = 64\\t^(2) =4\\t = 2`

So the ball hits the ground in 2s

Second question

• to find how long it takes the ball to fall 36 feet, we must set h(t) = 64 - 36 = 28

`-16t^(2) +64 = 28\\16t^(2) = 36\\t = (6)/(4) =1.5s`

So the ball hits the ground in 1.5s

Hope that helps!