SOLUTION: You toss a ball from 5 feet. The ball's velocity is 30 feet per second. You catch the ball at 6 feet. How long is the ball in the air?

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Question 670641: You toss a ball from 5 feet. The ball's velocity is 30 feet per second. You catch the ball at 6 feet. How long is the ball in the air?
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
You toss a ball from 5 feet. The ball's velocity is 30 feet per second. You catch the ball at 6 feet. How long is the ball in the air?
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h(t) = -16t^2 + 30t + 5
Solve for t at h(t) = 6 feet
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h(t) = -16t^2 + 30t + 5 = 6
-16t^2 + 30t - 1 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B30x%2B-1+=+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=%2830%29%5E2-4%2A-16%2A-1=836.

Discriminant d=836 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-30%2B-sqrt%28+836+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2830%29%2Bsqrt%28+836+%29%29%2F2%5C-16+=+0.0339479815749399
x%5B2%5D+=+%28-%2830%29-sqrt%28+836+%29%29%2F2%5C-16+=+1.84105201842506

Quadratic expression -16x%5E2%2B30x%2B-1 can be factored:
-16x%5E2%2B30x%2B-1+=+%28x-0.0339479815749399%29%2A%28x-1.84105201842506%29
Again, the answer is: 0.0339479815749399, 1.84105201842506. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B30%2Ax%2B-1+%29

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The 1st solution is at 6 ft on its way up.
The 2nd is the total time requested.
t =~ 1.841 seconds