Question

A fastball is hit straight up over home plate. The ball's height, h (in feet), from the ground is modeled by ℎ = −16푡 ଶ+103푡+5 where t is time (in seconds).

Answer 1

Question:

A fastball is hit straight up over home plate. The ball's height, h (in feet), from the ground is modeled by h(t)=-16t^2+80t+5, where t is measured in seconds. Write an equation to determine how long it will take for the ball to reach the ground.

Answer:

`t = 5.0625`

Explanation:

Given

`h(t)=-16t^2+80t+5`

Required

Find t when the ball hits the ground

This implies that h(t) = 0

So, we have:

`0=-16t^2+80t+5`

Reorder

`-16t^2+80t+5 = 0`

Using quadratic formula, we have:

`t = (-b\±√(b^2 - 4ac))/(2a)`

Where

`a = -16`
`b =80`
`c = 5`

So, we have:

`t = (-80\±√(80^2 - 4*-16*5))/(2*-16)`

`t = (-80\±√(6400 +320))/(-32)`

`t = (-80\±√(6720))/(-32)`

`t = (-80\±82.0)/(-32)`

This gives:

`t = (-80+82.0)/(-32)` or
`t = (-80-82.0)/(-32)`

`t = (2)/(-32)` or
`t = (-162)/(-32)`

`t = -(2)/(32)` or
`t = (162)/(32)`

But time can not be negative.

So, we have:

`t = (162)/(32)`

`t = 5.0625`

Hence, time to hit the ground is 5.0625 seconds