SOLUTION: a stone is thrown vertically upwards at a speed of 24 m/s. its height h meters after t seconds is given approximately by the formula h=24t-5t squared. Use this formula to find whe

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equation Customizable Word Problems -> SOLUTION: a stone is thrown vertically upwards at a speed of 24 m/s. its height h meters after t seconds is given approximately by the formula h=24t-5t squared. Use this formula to find whe      Log On


   

Question 281548: a stone is thrown vertically upwards at a speed of 24 m/s. its height h meters after t seconds is given approximately by the formula h=24t-5t squared. Use this formula to find when the stone is 27 meters up, and explain the double answer.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
a stone is thrown vertically upwards at a speed of 24 m/s. its height h meters after t seconds is given approximately by the formula h=24t-5t squared. Use this formula to find when the stone is 27 meters up, and explain the double answer.
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h(t) = 24t - 5t^2
-5t^2 + 24t - 27 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -5x%5E2%2B24x%2B-27+=+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=%2824%29%5E2-4%2A-5%2A-27=36.

Discriminant d=36 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-24%2B-sqrt%28+36+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2824%29%2Bsqrt%28+36+%29%29%2F2%5C-5+=+1.8
x%5B2%5D+=+%28-%2824%29-sqrt%28+36+%29%29%2F2%5C-5+=+3

Quadratic expression -5x%5E2%2B24x%2B-27 can be factored:
-5x%5E2%2B24x%2B-27+=+%28x-1.8%29%2A%28x-3%29
Again, the answer is: 1.8, 3. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-5%2Ax%5E2%2B24%2Ax%2B-27+%29

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at t=1.8 seconds it's at 27 meters and rising.
at t=2.4 seconds it's at its max height and starts to fall.
at t=3 seconds it's at 27 meters and falling.