What is the maximum height this rock reaches? When will the rock land in the lake?

Question

A hiker throws a rock from the top of a small cliff overlooking a lake. The height of the rock

(in feet) t seconds after it is thrown is given by the formula h(t) = −16t^2 + 64t + 80

What is the maximum height this rock reaches?

When will the rock land in the lake?

Answer 1

h'(t) = -32t + 64 = 0, t = 64/32 = 2 seconds to reach max height

plug t=2 into the given h(t) equation

h(2) = -16(2)^2 +64(2) + 80 = 144 feet = max height

It lands in the lake when h=0

h(t) = 0 = -16t^2 +64t + 80

-16t^2 + 64t + 80= 0 divide by -16

t^2 -4t -5 = 0 factor

(t-5)(t+1) = 0

t = 5 seconds for it to land in the lake