Vertical Motion

Question

A roofer drops shingles from a height of 52 feet into a pickup truck. The height, h (in feet) of the shingles above the ground can be modeled by h+-16t^2 + 52, where t is the time (in seconds) since the roofer dropped the shingles.

A. Solve the equation for t

B. After how many seconds will the shingles be 14 feet above the ground? Round to the nearest hundredth.

Answer 1

We know h = -16t² + 52

a) Solve for t

Subtract 52

h - 52 = -16t²

Divide by -16

(h - 52)/-16 = t²

Now take the square root (not sure how to make the symbol on here)

Square root of ((h - 52)/-16) = t

b) When will the shingle be 14 ft off the ground?

h = 14, so

14 = -16t² + 52

14 - 52 = -16t²

-38 = -16t²

-38/-16 = t²

t = square root (38/16) or approx. 1.54 seconds