SOLUTION: 11. At t=0 seconds, Vikki stood on the roof of a building and threw a penny in the air. The height in feet h(t) of the ball at t seconds is given by the formula H(t) = -16t2 + 96

Question 209090: 11. At t=0 seconds, Vikki stood on the roof of a building and threw a penny in the air. The height in feet h(t) of the ball at t seconds is given by the formula
H(t) = -16t2 + 96t +56
a) How tall is the building (hint: t=0)
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?

Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
At t=0 seconds, Vikki stood on the roof of a building and threw a penny in the air. The height in feet h(t) of the ball at t seconds is given by the formula
H(t) = -16t2 + 96t +56
a) How tall is the building (hint: t=0)
56 feet
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b) When is the ball at its highest point?
The equation is a parabola. The max height is at the vertex, when t = -b/2a
t = -96/-32 = 3 seconds
c) To what height does the ball travel?
h(3) = -144 + 288 + 56 = 200 feet
d) When does the ball strike the ground?
When h(t) = 0
-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:

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Use the positive value, x2, for time of impact.

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