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

Question

Mathematics

Andrew Parsons

24 September, 23:05

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

+1

Answers (1)

Know the Answer?

Siena Benitez · Answer 1

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)