The quadratic function h(t)=-16t^2 + 128t +144 shows the balls height about the ground, h(t), in feet, t, seconds after it was thrown.

Question

A person standing close to the edge on top of a 144-foot building throws a ball vertically upward. The quadratic function h(t)=-16t^2 + 128t +144 shows the balls height about the ground, h(t), in feet, t, seconds after it was thrown.

1. What is the maximum height of the ball?
2. How many seconds does it take until the ball hits the ground?

Answer 1

h(t) = -16t² + 128t + 144

 

(a)

 

Maximum height occurs at the vertex of the height-vs.-time parabola, which is at

 

t = -128/[2(-16)] sec = 4sec

 

Evaluate h(t) at this value of t to get h_max.

 h(4) = -16(4)² + 128(4) + 144=400 ft max height

(b)

 

Set h(t) = 0 and solve the quadratic equation for t. You will get a positive and a negative solution. Discard the negative solution, since time starts at t = 0.

 -16t² + 128t + 144=0

(t-9)(t+1)=0

t=9,-1

it take 9 secs until the ball hits the ground