Question

A catapult launches a boulder with an upward velocity of 184 ft/s. The height of the boulder (h) in feet after t seconds is given by the function h= -16t^2 + 184t + 20. How long does it take the boulder to reach its maximum height? What is the boulder's maximum hieght

Answer 1

The answer should be C.

Answer 2

For this case we have the following equation:
h = -16t ^ 2 + 184t + 20
Deriving we have:
h '= -32t + 184
We equal zero and clear t:
-32t + 184 = 0
32t = 184
t = 184/32
t = 5.75 s
Then, the maximum height is given by:
h (5.75) = -16 * (5.75) ^ 2 + 184 * (5.75) + 20
h (5.75) = 549 feet
Answer:
It takes the boulder to reach its maximum height about:
t = 5.75 s
the boulder's maximum hieght is:
h (5.75) = 549 feet