Question

A ball is thrown into the air with an upward velocity of 36 ft/s. Its height h in feet after t seconds is given by the function . 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?

a. 2.25 s; 9 ft
b. 1.13 s; 31.5 ft
c. 1.13 s; 69.75 ft
d.1.13 s; 29.25 ft

Answer 1

The answer is 1.13;29.25

Answer 2

h = -16t^2 + 36t + 9
At maximum height h' = 0,
h' = -32t + 36 = 0
32t = 36
t = 36/32 = 1.13 s.

Maximum height = -16(1.125)^2 + 36(1.125) + 9 = 29.25 ft

Answer is option d (1.13 s, 29.25 ft)