The height of the ball (ft), measured upward from the ground is
s(t) = 16t² + 64t + 80
where t = time when the ball is in the air.
When the ball hits the ground, s = 0. The time(s) when this occurs is given by
16t² + 64t + 80 = 0
Divide through by 16.
t² + 4t + 5 = 0
(t - 1)(t + 5) = 0
t = 1 or t = -5 s
Reject negative time, so that
t = 1 s
The velocity function is
v(t) = 64 + 32t
When t = 1 s, obtain
v(1) = 96 ft/s
Answer:
The ball hits the ground with velocity 96 ft/s.
