A ball is thrown into the air with an upward velocity of 28 ft/s. Its height (h) in feet after t seconds is given by the function h = –16t2 + 28t + 7. How long does it take the ball to reach its maximum height? What is the ball’s maximum height? Round to the nearest hundredth, if necessary. (1 point)

Question

A ball is thrown into the air with an upward velocity of 28 ft/s. Its height (h) in feet after t seconds is given by the function h = –16t2 + 28t + 7. How long does it take the ball to reach its maximum height? What is the ball’s maximum height? Round to the nearest hundredth, if necessary.  (1 point)

anonymous · Answer

Maximum height is achieved when v = dh/dt = 0.
 dh/dt = -32t + 28 = 0
 32t = 28
 t = 7/8 = 0.875 ≈ 0.88
 h = -16(7/8)^2 + 28(7/8) + 7 = 19.25
 0.88 s; 19.25 ft