# Juan hits a baseball. The equation h=-16t^2+120t models the height h, in feet, of the ball after t seconds. How long is the ball in the air?

Jul 15, 2017

When the ball returns to ground level, $h = 0$, so:

$- 16 {t}^{2} + 120 t = 0$

This is a quadratic equation we can solve to find the roots $t = 0$ or $t = 7.5$ $s$, which correspond to the beginning and end of the ball's flight.

#### Explanation:

For a quadratic in the form $a {x}^{2} + b x + c = 0$

We know:

$t = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2} a$

For

$- 16 {t}^{2} + 120 t = 0$

$a = - 16 , b = 120 , c = 0$

So:

$t = \frac{- 120 \pm \sqrt{{120}^{2} - 0}}{-} 32 = \frac{- 120 \pm 120}{32} = \frac{0}{-} 32 \mathmr{and} - \frac{240}{-} 32$

Therefore:

$t = 0$ or $t = 7.5$ $s$