Question

A ball is thrown into the air with an upward velocity of 48 ft/s. Its height h in feet after t seconds is given by the function h = -16t^2 + 48t + 6. How long does it take the ball to reach its maximum height? What is the ball's maximum height?

Answer 1

so you have to find the velocity (or first derivative) from the position function of h=-16t^2+48t+6

the velocity is -32t+48 which you then have to set equal to 0 in order to find t
-32t+48=0
-32t=-48
t=1.5

you then take your t value and sub it back into your original position function
-16(1.5)^2+48(1.5)+6 which will give you a maximum height of 42 feet

so the time it takes is 1.5 seconds to reach a maximum height of 42 feet