Solve application problems using quadratic functions.

Question

A person standing close to the edge on top of a 36-foot building throws a ball vertically upward. The quadratic function h(t) = -16t² + 140t + 36 models the ball’s height above the ground, h(t), in feet, t seconds after it was thrown.

A). What is the maximum height of the ball?

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

Answer 1

Hello Alex,

h(t) = -16t² + 140t + 36

for maximum height dh/dt =0

-32 t +140 =0

Gives t= 140/32 sec= 35/8 sec

Plug it in h(t)

H= 342.25 ft

For total time to touch the ground.

h(t) = 0 = -16t² + 140t + 36

Solving for t

16t^{2 -} 140t -36 =0

or 4t² -35 t-9=0

Two roots are t=9 sec and t= -0.25 sec , Negative time is ignored