SOLUTION: In July of 1997, the first cliff diving world championships were held in Brontallo, Switzerland. Participants performed acrobatic dives from heights up to 92 feet. Suppose a cliff

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Question 253269: In July of 1997, the first cliff diving world championships were held in Brontallo, Switzerland. Participants performed acrobatic dives from heights up to 92 feet. Suppose a cliff diver jumps from this height with an initial upward velocity of 5 feet per second. How much time does the diver have to perform acrobatic manuevers before hitting the water?
Answer by Greenfinch(383) About Me  (Show Source):
You can put this solution on YOUR website!
u = +5, s = -92, a = -32, t = ?
s = ut 1+ (at^2)/2
-92 = 5t +16t^2
16t^2 + 5t - 92=0
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case 16t%5E2%2B5t%2B-92+=+0) has the following solutons:

t%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%2A16%2A-92=5913.

Discriminant d=5913 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-5%2B-sqrt%28+5913+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%285%29%2Bsqrt%28+5913+%29%29%2F2%5C16+=+2.24675105337056
t%5B2%5D+=+%28-%285%29-sqrt%28+5913+%29%29%2F2%5C16+=+-2.55925105337056

Quadratic expression 16t%5E2%2B5t%2B-92 can be factored:
16t%5E2%2B5t%2B-92+=+16%28t-2.24675105337056%29%2A%28t--2.55925105337056%29
Again, the answer is: 2.24675105337056, -2.55925105337056. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B5%2Ax%2B-92+%29