Question

All ball is thrown into the air with an upward velocity of 24 ft/s. Its height h in feet after t seconds is given by the function h=-16t^2+24t+7. a. In how many seconds does the ball reach its maximum height? Round to the nearest hundredth if necessary. What is the ball's maximum height?

Answer 1

//I'm going to use differentiation to show you how to do this, although I would normally use mechanics.

dh/dt = -32t + 24
-32t + 24 = 0 when maximum
32t = 24
t = 24/32
t = 3/4

//To find the maximum height just substitute "t" in

h = -16 (9/16) + 24(3/4) + 7
h = -9 + 18 + 7
h = 16ft