SOLUTION: a ball is thrown straight up from a rooftop 240ft high. The ball misses the rooftop on the way down.When will the ball be at 120 ft. identify solution on a graph h=-16t^2+56t+240

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: a ball is thrown straight up from a rooftop 240ft high. The ball misses the rooftop on the way down.When will the ball be at 120 ft. identify solution on a graph h=-16t^2+56t+240      Log On


   

Question 544765: a ball is thrown straight up from a rooftop 240ft high. The ball misses the rooftop on the way down.When will the ball be at 120 ft. identify solution on a graph h=-16t^2+56t+240
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
h=-16t^2+56t+240
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Solve: -16t^2+56t+240 = 0
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-8(2t^2 - 7t + 30) = 0
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Quadratic Formula:
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t = [7 +- sqrt(49 - 4*2*30)]/4
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t = [7 +- sqrt(-191)]/4
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t = [7 + isqrt(191)]/4 or t = [7 - isqrt(191)]/4
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Cheers,
Stan H.
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Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
a ball is thrown straight up from a rooftop 240ft high. The ball misses the rooftop on the way down.When will the ball be at 120 ft. identify solution on a graph h=-16t^2+56t+240
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The 56 is the speed of the upward throw, 56 ft/sec
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h=-16t^2+56t+240
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Solve: -16t^2+56t+240 = 120
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-2t^2 + 7t + 15 = 0
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Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -2x%5E2%2B7x%2B15+=+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=%287%29%5E2-4%2A-2%2A15=169.

Discriminant d=169 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-7%2B-sqrt%28+169+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%287%29%2Bsqrt%28+169+%29%29%2F2%5C-2+=+-1.5
x%5B2%5D+=+%28-%287%29-sqrt%28+169+%29%29%2F2%5C-2+=+5

Quadratic expression -2x%5E2%2B7x%2B15 can be factored:
-2x%5E2%2B7x%2B15+=+%28x--1.5%29%2A%28x-5%29
Again, the answer is: -1.5, 5. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-2%2Ax%5E2%2B7%2Ax%2B15+%29

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Ignore the negative solution.
t = 5 seconds