Question

A tennis ball is dropped from the top of a tall building. The ball's height, in meters, t seconds after it is released is h(t)= -4.9t2 + 175.
1. Find h(4) and give real world meaning for the value. 2. When is the ball is dropped from 55 meters above the ground? 3. When does the ball hit the ground? Thanks!

Answer 1

1) h(4)=-4.9(4)^2 +175 = -4.9(16) +175 = 96.6 meters from the ground, perhaps the height of a small building?
2) h(t) = 55 = -4.9(t)^2 +175
55 - 175 = -4.9(t)^2
-120/-4.9 = t^2
(-24.49)^.5 = t = 4.9 seconds
3) the ball hits the ground when the distance from the ground is 0 meters
h(t) = 0 = -4.9(t)^2 +175
-175 = -4.9(t)^2
175/4.9 = t^2
(35.7)^.5 = t = 5.98 seconds