Question

A ball is thrown into the air with an upward velocity of 32 ft/s. Its height (h) in feet after t seconds is given by the function h= -16t^2 + 32t + 6. How long does it take the ball to reach its maximum height? What is the ball’s maximum height? Roun

Answer 1

For this case we have the following equation:
h = -16t ^ 2 + 32t + 6
Deriving we have:
h '= -32t + 32
We equal zero and clear t:
-32t + 32 = 0
32t = 32
t = 32/32
t = 1 s
Then, the maximum height is given by:
h (1) = -16 * (1) ^ 2 + 32 * (1) + 6
h (1) = 22 feet
Answer:
It takes the ball to reach its maximum height about:
t = 1 s
The ball's maximum height is:
h (1) = 22 feet