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

Question

A. How long did it take Morgan to reach her maximum height?  

B. What was the highest height that Morgan reached?

C. Morgan hit the water after how many seconds?

Answer 1

h'(t) = -32t + 16 = 0

t = 16/32 = 1/2 second to reach maximum height

max h(t) = h(1/2) = -16(1/2)^ + 16(1/2) + 480 = -4 + 8 + 480 = 484 feet = max height

h(t) = 0 = -16t^2 +16t + 480 = 0, divide by -16

t^2 -t - 30 = 0 factor

(t-6)(t+5) = 0

t =6 seconds to hit the water (ignore the -5 solution)