Question

During an experiment, a ball is dropped from a height of 205 feet. The formula h = -16t2 + h subscript 0 can be used to approximate the number of seconds t it takes for the ball to reach height h from an initial height of h subscript 0 in feet. Find the time it takes the ball to reach the ground.

Answer 1

4 seconds

Explanation:

`h = -16t^2 + h_0`

where h=height reached after t seconds

`h_0` = Initial Height of the ball

The ball is dropped from a height of 205 feet,

`h_0` = 205 feet

We want to determine the time it takes the ball to reach the ground.

i.e. when height of the ball, h=0

Substituting
`h_0` = 205 feet and h=0 into the formula

`h = -16t^2 + h_0`

`0 = -16t^2 + 205`

Add
`16t^2` to both sides

`0+16t^2 = -16t^2+16t^2 + 205\\16t^2=205`

Divide both sides by 16

`(16t^2)/(16)= (205)/(16)\\t^2=12.8125`

`t=√(12.8125) =3.58` ≈ 4 Seconds

It takes approximately 4 seconds for the ball to reach the ground.