SOLUTION: This is a summer math problem I was assigned. At t=0 seconds Vikki stood on the roof of a buildng and threw a ball in the air. The height of the ball at t seconds is gven by the fo

Question 211169: This is a summer math problem I was assigned. At t=0 seconds Vikki stood on the roof of a buildng and threw a ball in the air. The height of the ball at t seconds is gven by the formula H(t)=-16t2*+96t+56.
A:Answered
B:When is the ball at its highest point?
C:To what height does the ball travel?
D:When does the ball strike the ground?
*the number 2 is a square
Thank you in advance and the sooner this is answered the better.
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
This is a summer math problem I was assigned. At t=0 seconds Vikki stood on the roof of a buildng and threw a ball in the air. The height of the ball at t seconds is gven by the formula H(t)=-16t2*+96t+56.
A:Answered
B:When is the ball at its highest point?
There's more than one way to find that. One is to find the time when the ball returns to 56 feet, and the max height it 1/2 of that time, ie, it takes the ball the same amount of time going up as it does coming down.
H(t)=-16t2*+96t+56
56 = -16t2*+96t+56
-16t^2 + 96t = 0
t*(-16t + 96) = 0
t = 0 (the launch)
t = 6 seconds (on its way back down)
So the time at apogee (max height) is 3 seconds.
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C:To what height does the ball travel?
h(3) = -16*9 + 96*3 + 56
h(3) = 200 feet (apogee at t = 3 seconds)
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D:When does the ball strike the ground?
h(t) = 0 is ground level.
-16t2*+96t+56 = 0
-2t^2 + 12t + 7 = 0

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

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=200 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -0.535533905932738, 6.53553390593274. Here's your graph:

time of impact is 6.5355... seconds. Ignore the negative number.
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