SOLUTION: A baseball is thrown straight upwards with an initial velocity of 224 ft/s. At what time(s) does the ball reach 832 feet?

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Question 299593: A baseball is thrown straight upwards with an initial velocity of 224 ft/s.
At what time(s) does the ball reach 832 feet?
Found 2 solutions by helpnalgebra, Alan3354:
Answer by helpnalgebra(91) About Me  (Show Source):
You can put this solution on YOUR website!
you just divide the 224 into 832 = 3

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A baseball is thrown straight upwards with an initial velocity of 224 ft/s.
At what time(s) does the ball reach 832 feet?
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h(t) = -16t^2 + 224t gives the height in feet as a function of t in seconds.
832 = -16t^2 + 224t
-t^2 + 14t - 52 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B14x%2B-52+=+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=%2814%29%5E2-4%2A-1%2A-52=-12.

The discriminant -12 is less than zero. That means that there are no solutions among real numbers.

If you are a student of advanced school algebra and are aware about imaginary numbers, read on.


In the field of imaginary numbers, the square root of -12 is + or - sqrt%28+12%29+=+3.46410161513775.

The solution is , or
Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B14%2Ax%2B-52+%29

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Looks like it's on May 32nd.
It doesn't go that high, it's max height is 784 feet at 7 seconds.