SOLUTION: Foul Ball Suppose Charlie O'Brian of the Braves hits a baseball straight upward at 150 ft/sec from a height of 5ft. Use the formula to determine how long does it

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Question 246760: Foul Ball

Suppose Charlie O'Brian of the Braves hits a baseball straight upward at 150 ft/sec from a height of 5ft.

Use the formula to determine how long does it takes the ball to return to the earth.

Estimate the maximum height reached by the ball

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
Suppose Charlie O'Brian of the Braves hits a baseball straight upward at 150 ft/sec from a height of 5ft.
Use the formula to determine how long does it takes the ball to return to the earth.
h(t) =-16t^2 + 150t + 5 (h in feet, t in seconds)
To find the time of impact, set h(t) = 0
-16t^2 + 150t + 5 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B150x%2B5+=+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=%28150%29%5E2-4%2A-16%2A5=22820.

Discriminant d=22820 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-150%2B-sqrt%28+22820+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28150%29%2Bsqrt%28+22820+%29%29%2F2%5C-16+=+-0.0332156501954231
x%5B2%5D+=+%28-%28150%29-sqrt%28+22820+%29%29%2F2%5C-16+=+9.40821565019542

Quadratic expression -16x%5E2%2B150x%2B5 can be factored:
-16x%5E2%2B150x%2B5+=+%28x--0.0332156501954231%29%2A%28x-9.40821565019542%29
Again, the answer is: -0.0332156501954231, 9.40821565019542. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B150%2Ax%2B5+%29


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Sub t for x, the solver uses x
Ignore the negative time.
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Estimate the maximum height reached by the ball
That's at the vertex of the parabola.
t = -b/2a = -150/-32
t = 75/16 seconds
h(75/16) = -16*(75/16)^2 + 150*75/16 + 5
h = - 5625/16 + 11250/16 + 80/16
h = 5705/16 feet
h = 356.5625 feet exactly