SOLUTION: A rocket is launched from atop a 43-foot cliff with an initial velocity of 70 feet per second. The height of the rocket t seconds after launch is given by the equation h = -16t^2 +

Algebra ->  Algebra  -> Quadratic Equations and Parabolas -> SOLUTION: A rocket is launched from atop a 43-foot cliff with an initial velocity of 70 feet per second. The height of the rocket t seconds after launch is given by the equation h = -16t^2 +      Log On

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Question 210045: A rocket is launched from atop a 43-foot cliff with an initial velocity of 70 feet per second. The height of the rocket t seconds after launch is given by the equation h = -16t^2 + 70t + 43. Graph the equation to find out how long after the rocket is launched it ill hit the ground. Estimate your answer to the nearest tenth of a second.
Answer by Alan3354(30993) About Me  (Show Source):
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A rocket is launched from atop a 43-foot cliff with an initial velocity of 70 feet per second. The height of the rocket t seconds after launch is given by the equation h = -16t^2 + 70t + 43. Graph the equation to find out how long after the rocket is launched it ill hit the ground. Estimate your answer to the nearest tenth of a second.
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h = -16t^2 + 70t + 43
Set h = 0 and solve for t
-16t^2 + 70t + 43 = 0
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B70x%2B43+=+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=%2870%29%5E2-4%2A-16%2A43=7652.

Discriminant d=7652 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-70%2B-sqrt%28+7652+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%2870%29%2Bsqrt%28+7652+%29%29%2F2%5C-16+=+-0.54611596607863
x%5B2%5D+=+%28-%2870%29-sqrt%28+7652+%29%29%2F2%5C-16+=+4.92111596607863

Quadratic expression -16x%5E2%2B70x%2B43 can be factored:
-16x%5E2%2B70x%2B43+=+%28x--0.54611596607863%29%2A%28x-4.92111596607863%29
Again, the answer is: -0.54611596607863, 4.92111596607863. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B70%2Ax%2B43+%29

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Use the positive number.
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BTW, rockets have motors and they accelerate when launched. This is a ballistics problem, and the "rocket" just rises and falls due to initial forces and gravity.
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