Mrs. D jumped off a cliff into the ocean with Mrs. H. Her height as a function of time could be modeled by the function h(t)=-16t²+16t+480 (where t is the time in seconds and h is the height in feet.)

Question

Part (a) How long did it take for Mrs. D to reach her maximum height?

Part (b) What was her maximum height?

Part (c) What her was her initial height?

Part (d) What was her height at 5 seconds?

Answer 1

a) 1/2 second to reach maximum height, apparently she jumped 4 feet into the air upward before gravity took over completely

b) max height 484 feet

c) initial height was 480 feet

d) her height after 5 second = 0, when she hits the ocean

take the derivative of the quadratic and set = 0, solve for t which is 1/2 second for max height

plug 1/2 into the original quadratic to get 484, which is 4 feet above her initial height of 480, the constant term in the quadratic.

plug t=5 into the quadratic to get zero height, h(5) = 0