SOLUTION: When a ball is thrown, its height in feet h after t seconds is given by the equation h=vt-16t^2 where v is the initial upwards velocity in feet per second. If v=9 feet per

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Question 350709: When a ball is thrown, its height in feet h after t seconds is given by the equation
h=vt-16t^2
where v is the initial upwards velocity in feet per second. If v=9 feet per second, find all values of t for which h=1 foot. Do not round any intermediate steps. Round your answer to 2 decimal places.
Answer by nerdybill(6958) About Me  (Show Source):
You can put this solution on YOUR website!
When a ball is thrown, its height in feet h after t seconds is given by the equation
h=vt-16t^2
where v is the initial upwards velocity in feet per second. If v=9 feet per second, find all values of t for which h=1 foot. Do not round any intermediate steps. Round your answer to 2 decimal places.
.
h=vt-16t^2
Substitute in the value for v:
h=9t-16t^2
Substitute in the value for h:
1=9t-16t^2
Solving for t:
1=9t-16t^2
16t^2+1=9t
16t^2-9t+1=0
Solve using the quadratic formula. Doing so yields
t = {0.41, 0.15} seconds
.
Detail of quadratic follows:
Solved by pluggable solver: SOLVE quadratic equation with variable
Quadratic equation at%5E2%2Bbt%2Bc=0 (in our case 16t%5E2%2B-9t%2B1+=+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=%28-9%29%5E2-4%2A16%2A1=17.

Discriminant d=17 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--9%2B-sqrt%28+17+%29%29%2F2%5Ca.

t%5B1%5D+=+%28-%28-9%29%2Bsqrt%28+17+%29%29%2F2%5C16+=+0.410097050800552
t%5B2%5D+=+%28-%28-9%29-sqrt%28+17+%29%29%2F2%5C16+=+0.152402949199448

Quadratic expression 16t%5E2%2B-9t%2B1 can be factored:
16t%5E2%2B-9t%2B1+=+16%28t-0.410097050800552%29%2A%28t-0.152402949199448%29
Again, the answer is: 0.410097050800552, 0.152402949199448. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+16%2Ax%5E2%2B-9%2Ax%2B1+%29