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=-16t^2+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.

A. 1.75 s; 7 ft
B. 0.88 s; 43.75 ft
C. 0.88 s; 17.5 ft
D. 0.88 s; 19.25 ft

Answer 1

The Answer is D:

h = -16t^2 + 28t + 7
h' = -32t + 28

-32t + 28 = 0

-32t = -28

t = .875 seconds

h(.875) = -16(.875^2) + 28(.875) + 7

h(.875) = 19.25 ft
Rounding time to nearest hundredth gives max at (.88s, 19.25ft)