SOLUTION: A ball is thrown upward from the top of a building. The ball's height above the ground after T seconds is given by the function: h(t) = -16t^2+48t+32. A. What is the initial heigh

Question 730161: A ball is thrown upward from the top of a building. The ball's height above the ground after T seconds is given by the function: h(t) = -16t^2+48t+32.
A. What is the initial height (i.e. the height of the building)?
B. How high did the ball go?
C. When does the ball hit the ground?
Answer by nerdybill(7384) (Show Source): You can put this solution on YOUR website!
A ball is thrown upward from the top of a building. The ball's height above the ground after T seconds is given by the function: h(t) = -16t^2+48t+32.
A. What is the initial height (i.e. the height of the building)?
initial height is when t=0:
h(t) = -16t^2+48t+32
h(0) = -16(0)^2+48(0)+32
h(0) = 32 feet
.
B. How high did the ball go?
vertex is at max:
time, at vertex:
t = -b/(2a)
t = -48/(2(-16))
t = -48/(-32)
t = 3/2
.
Height at t=3/2:
h(3/2) = -16(3/2)^2+48(3/2)+32
h(3/2) = -16(9/4)+24(3)+32
h(3/2) = -4(9)+24(3)+32
h(3/2) = -36+72+32
h(3/2) = 68 feet
.
C. When does the ball hit the ground?
set h(t) to zero and solve for t:
h(t) = -16t^2+48t+32
0 = -16t^2+48t+32
0 = t^2-3t-2
solve by applying the "quadratic formula" to get:
t = {3.56, -0.56}
throw out the negative solution (extraneous) leaving
t = 3.56 seconds
.
Details of quadratic formula follows:

Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=17 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: 3.56155281280883, -0.56155281280883. Here's your graph:

RELATED QUESTIONS
A ball is thrown upward from the top of a building. The ball's height above the ground... (answered by josmiceli)

A ball is thrown upward from the top of a building. The ball's height above the ground... (answered by richwmiller)

A ball is thrown vertically upwards from the top of a school building. It�s height, h... (answered by ikleyn)

Supporting algebraic work must accompany your answers. A ball is thrown vertically... (answered by Alan3354)

a ball is thrown upward from the top of a 64-foot-high building. the ball is 96 feet... (answered by Boreal)

A ball is thrown vertically upward from the top of a building 96 feet tall with an... (answered by ankor@dixie-net.com,ikleyn)

A ball is thrown vertically upward from the top of a building 96 feet tall with an... (answered by Alan3354)

A ball is thrown upward from the top of a 240 foot building. The ball is 256 feet above... (answered by Alan3354,josmiceli)

H(t)= -5t^2 + at + b At time t=0, a ball was thrown upward from the top of a building.... (answered by ikleyn)