SOLUTION: A coin is tossed downward with an initial velocity of 30 m/sec from an altitude of 75m. Approximately how long does it take the ball to reach the ground? use 4.9t^2+v0t=s

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A coin is tossed downward with an initial velocity of 30 m/sec from an altitude of 75m. Approximately how long does it take the ball to reach the ground? use 4.9t^2+v0t=s      Log On


   

Question 1061530: A coin is tossed downward with an initial velocity of 30 m/sec from an altitude of 75m. Approximately how long does it take the ball to reach the ground? use 4.9t^2+v0t=s
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A coin is tossed downward with an initial velocity of 30 m/sec from an altitude of 75m. Approximately how long does it take the ball to reach the ground? use 4.9t^2+v0t=s
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Coin or ball, either way.
Use + for height and + for ascending.
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Use s(t) = -4.9t^2 + vot + h Where vo is + upward and negative downward & h = 75.
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s(t) = -4.9t^2 - 30t + 75 = 0
s(t) = 0 at impact
-4.9t^2 - 30t + 75 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -4.9x%5E2%2B-30x%2B75+=+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=%28-30%29%5E2-4%2A-4.9%2A75=2370.

Discriminant d=2370 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28--30%2B-sqrt%28+2370+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28-30%29%2Bsqrt%28+2370+%29%29%2F2%5C-4.9+=+-8.02884140597473
x%5B2%5D+=+%28-%28-30%29-sqrt%28+2370+%29%29%2F2%5C-4.9+=+1.90639242638289

Quadratic expression -4.9x%5E2%2B-30x%2B75 can be factored:
-4.9x%5E2%2B-30x%2B75+=+%28x--8.02884140597473%29%2A%28x-1.90639242638289%29
Again, the answer is: -8.02884140597473, 1.90639242638289. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-4.9%2Ax%5E2%2B-30%2Ax%2B75+%29

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Ignore the negative solution
t =~ 1.906 seconds