SOLUTION: At 9:45 am Margie threw a ball upwards while standing on a platform 75 ft off of the ground. The trajectory after t seconds follows the equation: h(t) = –0.6t2 + 108t + 75. a. Wh

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Question 762872: At 9:45 am Margie threw a ball upwards while standing on a platform 75 ft off of the ground. The trajectory after t seconds follows the equation: h(t) = –0.6t2 + 108t + 75.
a. What will be the maximum height of the ball? __________
b. How long will it take the ball reach its maximum height? __________
c. At what time will the ball hit the ground? _________
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Margie threw a ball upwards while standing on a platform 75 ft off of the ground. The trajectory after t seconds follows the equation:
h(t) = –0.6t2 + 108t + 75.
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b. How long will it take the ball reach its maximum height?
The equation is of a parabola.
The max ht is the vertex.
The vertex is on the axis of symmetry, t = -b/2a
t = -108/(2*-0.6) = 90 seconds
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a. What will be the maximum height of the ball?
Max ht = h(90)
= -0.6*90^2 + 108*90 + 75
= 4935 ft
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c. At what time will the ball hit the ground?
When h(t) = 0
h(t) = –0.6t^2 + 108t + 75 = 0
6t^2 - 1080t - 750 = 0
t^2 - 180t - 125 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 1x%5E2%2B-180x%2B-125+=+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=%28-180%29%5E2-4%2A1%2A-125=32900.

Discriminant d=32900 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--180%2B-sqrt%28+32900+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-180%29%2Bsqrt%28+32900+%29%29%2F2%5C1+=+180.691785736085
x%5B2%5D+=+%28-%28-180%29-sqrt%28+32900+%29%29%2F2%5C1+=+-0.691785736085265

Quadratic expression 1x%5E2%2B-180x%2B-125 can be factored:
1x%5E2%2B-180x%2B-125+=+%28x-180.691785736085%29%2A%28x--0.691785736085265%29
Again, the answer is: 180.691785736085, -0.691785736085265. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+1%2Ax%5E2%2B-180%2Ax%2B-125+%29

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t =~ 180.69 seconds
Ignore the negative solution