math 151 question

Question

A person standing close to the edge on top of a 80-foot building throws a ball vertically upward. The quadratic function  models the ball's height about the ground, , in feet,  seconds after it was thrown.a)



What is the maximum height of the ball?(Round your answer to the nearest hundredths.)   (feet)

How many seconds does it take until the ball hits the ground?   seconds

Answer 1

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

take the derivative and set = 0. At maximum height velocity is zero

v(t) = h'(t) = -32t + 64 = 0

t-2 = 0

t = 2 seconds to reach maximum height

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

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

t^2 -4t = 80/16 = 5

complete the square

t^2 -4t + 4 = 5+4

(t-2)^2 = 9

take square roots of both sides

t-2 = 3 (ignore the negative square root)

t = 5 seconds to hit the ground