A basketball bounces off the ground. The balls height y (in feet) after t seconds can be modled by y=-16t^2+40t. How many seconds is the ball in the air?

Question

How many seconds will it take to reach its maximum height? How do you know that

Answer 1

For total time in the air, set 

 

y(t) = 0 

 

and solve for t. 

 

0 = -16t² + 40t = t(-16t + 40) ⇒

 

-16t + 40 = 0

 

t = 40/16 sec = ? sec

 

For time to max height, find the t-coordinate of the vertex of the y-vs.-t parabola.

 

t = -40/[2(-16)] sec = ? sec

 

Note the vertex is a maximum of the y-vs.-t parabola.