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

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) (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
---------------------------------
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 (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=25049 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -0.789648711306167, 9.10214871130617. Here's your graph:

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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.

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