SOLUTION: A rocket is launched from atop a 115-foot cliff with an initial velocity of 133 ft/s. a. Substitute the values into the vertical motion formula h = –16t2 + vt + c. Let h = 0. b

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: A rocket is launched from atop a 115-foot cliff with an initial velocity of 133 ft/s. a. Substitute the values into the vertical motion formula h = –16t2 + vt + c. Let h = 0. b      Log On


   

Question 289064: A rocket is launched from atop a 115-foot cliff with an initial velocity of 133 ft/s.
a. Substitute the values into the vertical motion formula h = –16t2 + vt + c. Let h = 0.
b. Use the quadratic formula to find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.
Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
A rocket is launched from atop a 115-foot cliff with an initial velocity of 133 ft/s.
a. Substitute the values into the vertical motion formula h = –16t2 + vt + c. Let h = 0.
h(t) = -16t^2 + 133t + 115 = 0
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b. Use the quadratic formula to find out how long the rocket will take to hit the ground after it is launched. Round to the nearest tenth of a second.
Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)
Quadratic equation ax%5E2%2Bbx%2Bc=0 (in our case -16x%5E2%2B133x%2B115+=+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=%28133%29%5E2-4%2A-16%2A115=25049.

Discriminant d=25049 is greater than zero. That means that there are two solutions: +x%5B12%5D+=+%28-133%2B-sqrt%28+25049+%29%29%2F2%5Ca.

x%5B1%5D+=+%28-%28133%29%2Bsqrt%28+25049+%29%29%2F2%5C-16+=+-0.789648711306167
x%5B2%5D+=+%28-%28133%29-sqrt%28+25049+%29%29%2F2%5C-16+=+9.10214871130617

Quadratic expression -16x%5E2%2B133x%2B115 can be factored:
-16x%5E2%2B133x%2B115+=+%28x--0.789648711306167%29%2A%28x-9.10214871130617%29
Again, the answer is: -0.789648711306167, 9.10214871130617. Here's your graph:
graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-16%2Ax%5E2%2B133%2Ax%2B115+%29

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Ignore the negative value
t =~ 9.1 seconds
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This is not a rocket, rockets have thrust engines and accelerate upward.
This is just an unpowered ballistics problem.