SOLUTION: A model rocket is launched with an initial upward velocity of 50 m/s. The rocket's height h (in meters) after t seconds is given by the following, h = 50t - 5(t,s) Find all t

Algebra ->  Rate-of-work-word-problems -> SOLUTION: A model rocket is launched with an initial upward velocity of 50 m/s. The rocket's height h (in meters) after t seconds is given by the following, h = 50t - 5(t,s) Find all t      Log On


   

Question 1186378: A model rocket is launched with an initial upward velocity of 50 m/s. The rocket's height h (in meters) after t seconds is given by the following,
h = 50t - 5(t,s)
Find all the values of t for which the rocket's height is 30 meters.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A model rocket is launched with an initial upward velocity of 50 m/s. The rocket's height h (in meters) after t seconds is given by the following,
h = 50t - 5(t,s)
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Find all the values of t for which the rocket's height is 30 meters.
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IDK what (t,s) means.
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h(t) = 50t - 5t^2 = 30
-t^2 + 10t - 6 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -1x%5E2%2B10x%2B-6+=+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=%2810%29%5E2-4%2A-1%2A-6=76.

Discriminant d=76 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-10%2B-sqrt%28+76+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2810%29%2Bsqrt%28+76+%29%29%2F2%5C-1+=+0.641101056459326
x%5B2%5D+=+%28-%2810%29-sqrt%28+76+%29%29%2F2%5C-1+=+9.35889894354067

Quadratic expression -1x%5E2%2B10x%2B-6 can be factored:
-1x%5E2%2B10x%2B-6+=+%28x-0.641101056459326%29%2A%28x-9.35889894354067%29
Again, the answer is: 0.641101056459326, 9.35889894354067. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B10%2Ax%2B-6+%29

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t = smaller value ascending, larger value descending