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

Algebra ->  Quadratic Equations and Parabolas -> 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      Log On


   

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) About Me  (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 ax%5E2%2Bbx%2Bc=0 (in our case -2x%5E2%2B12x%2B7+=+0) has the following solutons:

x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca

For these solutions to exist, the discriminant b%5E2-4ac should not be a negative number.

First, we need to compute the discriminant b%5E2-4ac: b%5E2-4ac=%2812%29%5E2-4%2A-2%2A7=200.

Discriminant d=200 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-12%2B-sqrt%28+200+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2812%29%2Bsqrt%28+200+%29%29%2F2%5C-2+=+-0.535533905932738
x%5B2%5D+=+%28-%2812%29-sqrt%28+200+%29%29%2F2%5C-2+=+6.53553390593274

Quadratic expression -2x%5E2%2B12x%2B7 can be factored:
-2x%5E2%2B12x%2B7+=+%28x--0.535533905932738%29%2A%28x-6.53553390593274%29
Again, the answer is: -0.535533905932738, 6.53553390593274. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B12%2Ax%2B7+%29

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