SOLUTION: A Ball is thrown upward from a height of 15 ft. with an initial upward velocity of 5 ft a sec. Use the formula h=-16t squared+vt+s to find out how long it will take for the ball to

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A Ball is thrown upward from a height of 15 ft. with an initial upward velocity of 5 ft a sec. Use the formula h=-16t squared+vt+s to find out how long it will take for the ball to      Log On


   

Question 440852: A Ball is thrown upward from a height of 15 ft. with an initial upward velocity of 5 ft a sec. Use the formula h=-16t squared+vt+s to find out how long it will take for the ball to hit the ground?
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
h(t) = -16t^2 + 5t + 15
It impacts when h=0
-16t^2 + 5t + 15 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B5x%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=%285%29%5E2-4%2A-16%2A15=985.

Discriminant d=985 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+985+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%285%29%2Bsqrt%28+985+%29%29%2F2%5C-16+=+-0.824522176654701
x%5B2%5D+=+%28-%285%29-sqrt%28+985+%29%29%2F2%5C-16+=+1.1370221766547

Quadratic expression -16x%5E2%2B5x%2B15 can be factored:
-16x%5E2%2B5x%2B15+=+%28x--0.824522176654701%29%2A%28x-1.1370221766547%29
Again, the answer is: -0.824522176654701, 1.1370221766547. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B5%2Ax%2B15+%29

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Ignore the negative solution
t = 1.137 seconds

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A Ball is thrown upward from a height of 15 ft. with an initial upward velocity of 5 ft a sec. Use the formula h=-16t squared+vt+s to find out how long it will take for the ball to hit the ground?
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h=-16t squared+vt+s
h(t) = -16t^2+5t+15
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Height is zero when the ball hits the ground:
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Solve: -16t^2+5t+15 = 0
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Use Quadratic Formula:
t = [-5 +- sqrt(25-4*-16*15)]/(-32)
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t = [-5 +- sqrt(985)]/(-32)
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Positive solution:
t = [-5-31.38]/(-32)
t = 1.1370 seconds
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Cheers,
Stan H.