Question

When serving in tennis a player tosses the tennis ball vertically in the . The height h of the ball after t seconds is given by the quadratic function h(t)=-5t^2+7t (the height is measured in meters from the point of the toss.)

a. How high in the air does the ball go?
b. Assume that the player hits the ball on its way down when it's 0.6m above the point of the toss. For how many seconds is the ball in the air between the toss and the serve?

Answer 1

a.) For maximum height, h'(t) = -10t + 7 = 0
t = 7/10
Maximum height h(t) = -5(7/10)^2 + 7(7/10) = -5(49/100) + 49/10 = -49/20 + 49/10 = 49/20 = 2 9/20 meters = 2.45 meters.

b.) When h(t) = 0.6m
0.6 = -5t^2 + 7t
5t^2 - 7t + 0.6 = 0
t = 1.308 or 0.092
The ball has stayed 1.308 seconds in air.