SOLUTION: The equation h=-16t^-64t+250 (i used the symbol ^ to represent t squared) gives the height of a ball, thrown downward from the top of a 250-ft building with an initial velocity of

Algebra ->  Linear-equations -> SOLUTION: The equation h=-16t^-64t+250 (i used the symbol ^ to represent t squared) gives the height of a ball, thrown downward from the top of a 250-ft building with an initial velocity of      Log On


   

Question 473190: The equation h=-16t^-64t+250 (i used the symbol ^ to represent t squared) gives the height of a ball, thrown
downward from the top of a 250-ft building with an initial velocity of 64 ft/s.
Find the time it takes for the ball to reach a height of 100 ft. Round your answer
to the nearest thousandth.
Thank you in advance for your hardwork.
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The equation h=-16t^-64t+250 (i used the symbol ^ to represent t squared) gives the height of a ball, thrown
downward from the top of a 250-ft building with an initial velocity of 64 ft/s.
Find the time it takes for the ball to reach a height of 100 ft. Round your answer
to the nearest thousandth.
-----------
Use ^2 for squared, ^3 for cubed, etc.
--------------------
h(t) = -16t^2-64t+250 = 100
8t^2 + 32t - 75 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case 8x%5E2%2B32x%2B-75+=+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=%2832%29%5E2-4%2A8%2A-75=3424.

Discriminant d=3424 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-32%2B-sqrt%28+3424+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2832%29%2Bsqrt%28+3424+%29%29%2F2%5C8+=+1.65718470958195
x%5B2%5D+=+%28-%2832%29-sqrt%28+3424+%29%29%2F2%5C8+=+-5.65718470958195

Quadratic expression 8x%5E2%2B32x%2B-75 can be factored:
8x%5E2%2B32x%2B-75+=+%28x-1.65718470958195%29%2A%28x--5.65718470958195%29
Again, the answer is: 1.65718470958195, -5.65718470958195. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+8%2Ax%5E2%2B32%2Ax%2B-75+%29

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t = 1.657 seconds
Ignore the negative answer.

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The equation h=-16t^2-64t+250 (i used the symbol ^ to represent t squared) gives the height of a ball, thrown
downward from the top of a 250-ft building with an initial velocity of 64 ft/s.
Find the time it takes for the ball to reach a height of 100 ft. Round your answer to the nearest thousandth.
---
Set the height equal to 100 and solve for "t":
--------
-16t^2-64t+250 = 100
---
-16t^2-64t + 150 = 0
---
Divide thru by -2 to get:
8t^2 + 32t - 75 = 0
-----
Use the quadratic formula to get:
t = 1.657 seconds
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Cheers,
Stan H.
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