Question

Sofia hits a softball straight up. the equation h= -16t^2 + 90t models the height h, in feet, of the ball after t seconds. How long is the ball in the air?

Answer 1

It is in the air 5.625 seconds.

Using the quadratic formula,

$t=\frac{-b\pm \sqrt{b^2-4ac}}{2a} \\ \\=\frac{-90\pm \sqrt{90^2-4(-16)(0)}}{2(-16)} \\ \\=\frac{-90\pm \sqrt{8100-0}}{-32} \\ \\=\frac{-90\pm \sqrt{8100}}{-32}=\frac{-90\pm90}{-32} \\ \\=\frac{-90+90}{-32}\text{ or }\frac{-90-90}{-32}=\frac{0}{32}\text{ or }\frac{-180}{-32} \\ \\=0\text{ or }5.625$

0 is when the ball is first launched, 5.625 is when it hits the ground again.