A catapult launches a boulder with an upward velocity of 112 ft/s. The height of the boulder, h, in feet after t seconds is given by the function.

How long does it take the boulder to reach its maximum height? What is the boulder's maximum height? Round to the nearest hundredth, if necessary. h=-16t^2+112t+30

A. 7 s; 30 ft

B. 3.5 s; 366 ft

C. 3.5 s; 618 ft

D. 3.5 s; 226 ft

Question

Mathematics

Lana Potts

26 April, 07:58

A catapult launches a boulder with an upward velocity of 112 ft/s. The height of the boulder, h, in feet after t seconds is given by the function.

How long does it take the boulder to reach its maximum height? What is the boulder's maximum height? Round to the nearest hundredth, if necessary. h=-16t^2+112t+30

A. 7 s; 30 ft

B. 3.5 s; 366 ft

C. 3.5 s; 618 ft

D. 3.5 s; 226 ft

+5

Answers (1)

Know the Answer?

Annalise Reid · Answer 1

To determine the time it takes for boulder to reach its maximum height, derive the equation and equate to zero.

h = - 16t² + 112t + 30

dh / dt = 0 = - 32t + 112

The value of t from the equation above is 3.5 s. Substitute this value of t to the original question,

h = - 16 (3.5 s) ² + 112 (3.5 s) + 30 = 226 ft

Thus, the answer is letter D.