Question

The height of a pop fly ball over the time after the ball is hit is modeled by the function, h(t) = −16t2+81t + 5, where h is the ball’s height in feet above the ground and t is the time in seconds after the ball is hit. Use the quadratic formula to find how many seconds it takes for the ball to hit the ground.

Answer 1

We have been given that the height of a pop fly ball over the time after the ball is hit is modeled by the function, $h(t) =-16t^2+81t+5$, where h is the ball’s height in feet above the ground and t is the time in seconds after the ball is hit.

We are asked to find the time it will take or the ball to hit the ground.

We will use quadratic formula to solve our given problem.

$x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}$

For our given problem, $a=-16,b=81\text{ and }c=5$.

$x=\frac{-81\pm \sqrt{81^2-4(-16)(5)}}{2(-16)}$

$x=\frac{-81\pm \sqrt{6561+320}}{-32}$

$x=\frac{-81\pm \sqrt{6881}}{-32}$

$x=\frac{-81+\sqrt{6881}}{-32},\frac{-81+\sqrt{6881}}{-32}$

$x=-0.06099,5.12349$

Since time cannot be negative, so we will take only positive value of t.

$x\approx 5.12$

Therefore, it will take approximately 5.12 seconds for the ball to hit the ground.