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=(-b\pm √(b^2-4ac))/(2a) \\ \\=(-90\pm √(90^2-4(-16)(0)))/(2(-16)) \\ \\=(-90\pm √(8100-0))/(-32) \\ \\=(-90\pm √(8100))/(-32)=(-90\pm90)/(-32) \\ \\=(-90+90)/(-32)\text{ or }(-90-90)/(-32)=(0)/(32)\text{ or }(-180)/(-32) \\ \\=0\text{ or }5.625`

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