SOLUTION: Suppose a ball is thrown straight up at a speed of 50 feet per second. The time in seconds that it takes for the ball to hit the ground can be found by solving the equation 5 + 50t

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Question 456241: Suppose a ball is thrown straight up at a speed of 50 feet per second. The time in seconds that it takes for the ball to hit the ground can be found by solving the equation 5 + 50t - 16t^2 = 0. Approximately how long does it take for the ball to hit the ground?
Answer by nerdybill(7384) About Me  (Show Source):
You can put this solution on YOUR website!
5 + 50t - 16t^2 = 0
0 = 16t^2-50t-5
apply the "quadratic formula" to get:
t = {3.222, -0.097}
we can throw out the negative answer leaving
t = 3.2 seconds
.
details of quadratic to follow:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case 16t%5E2%2B-50t%2B-5+=+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=%28-50%29%5E2-4%2A16%2A-5=2820.

Discriminant d=2820 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--50%2B-sqrt%28+2820+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%28-50%29%2Bsqrt%28+2820+%29%29%2F2%5C16+=+3.22198975591897
t%5B2%5D+=+%28-%28-50%29-sqrt%28+2820+%29%29%2F2%5C16+=+-0.0969897559189692

Quadratic expression 16t%5E2%2B-50t%2B-5 can be factored:
16t%5E2%2B-50t%2B-5+=+16%28t-3.22198975591897%29%2A%28t--0.0969897559189692%29
Again, the answer is: 3.22198975591897, -0.0969897559189692. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B-50%2Ax%2B-5+%29