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).

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.

Step-by-step explanation:

Given

Required

Find t when the ball hits the ground

This implies that h(t) = 0

So, we have:

Reorder

Using quadratic formula, we have:

Where

So, we have:

This gives:

or

or

or

But time can not be negative.

So, we have:

Hence, time to hit the ground is 5.0625 seconds