SOLUTION: The height of an object is given by h=-16t^2+v^0t+h^0 ft. after t seconds, where v^0 is the initial velocity of the object in ft./sec and h^0 is the initial height of the object in

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Question 215961This question is from textbook
: The height of an object is given by h=-16t^2+v^0t+h^0 ft. after t seconds, where v^0 is the initial velocity of the object in ft./sec and h^0 is the initial height of the object in feet.
An object is thrown upwards from the top of a 650ft. building at an initial velocity of 64 ft./sec.
a) For what t>0 is the object feet from the ground?

b)For what t.0 is the object on the ground?
This question is from textbook

Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
The height of an object is given by h=-16t^2+v^0t+h^0 ft. after t seconds, where v^0 is the initial velocity of the object in ft./sec and h^0 is the initial height of the object in feet.
An object is thrown upwards from the top of a 650ft. building at an initial velocity of 64 ft./sec.
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h(t) = -16t^2 + 64t + 650
a) For what t>0 is the object feet from the ground?
?? How many feet?
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b)For what t.0 is the object on the ground?
-16t^2 + 64t + 650 = 0
-8t^2 + 32t + 325 = 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%2B325+=+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%2A-8%2A325=11424.

Discriminant d=11424 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-32%2B-sqrt%28+11424+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2832%29%2Bsqrt%28+11424+%29%29%2F2%5C-8+=+-4.68019460794369
x%5B2%5D+=+%28-%2832%29-sqrt%28+11424+%29%29%2F2%5C-8+=+8.68019460794369

Quadratic expression -8x%5E2%2B32x%2B325 can be factored:
-8x%5E2%2B32x%2B325+=+%28x--4.68019460794369%29%2A%28x-8.68019460794369%29
Again, the answer is: -4.68019460794369, 8.68019460794369. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-8%2Ax%5E2%2B32%2Ax%2B325+%29

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t = ~ 8.68 seconds