SOLUTION: A rocket is launched from atop a 101-foot cliff with an initial velocity of 116 ft/s. A. substitute the values into the vertical motion formula h=-16t^2+vt+c.Let h=0. B. Use

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Question 308557: A rocket is launched from atop a 101-foot cliff with an initial velocity of 116 ft/s.
A. substitute the values into the vertical motion formula h=-16t^2+vt+c.Let h=0.
B. Use the quadratic formula 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 nerdybill(7384) (Show Source):
You can put this solution on YOUR website!
A rocket is launched from atop a 101-foot cliff with an initial velocity of 116 ft/s.
A. substitute the values into the vertical motion formula h=-16t^2+vt+c.Let h=0.
h=-16t^2 + 116t + 101
.
B. Use the quadratic formula find out how long the rocket will take to hit the ground after it is launched.Round to the nearest tenth of a second.
0=-16t^2 + 116t + 101
Applying the quadratic formula yields:
t = {-0.8, 8.0}
We can toss out the negative solution leaving:
t = 8.0 seconds
.
Details of quadratic formula follows:

Solved by pluggable solver: SOLVE quadratic equation with variable

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=19920 is greater than zero. That means that there are two solutions: .

Quadratic expression can be factored:

Again, the answer is: -0.785569691094338, 8.03556969109434. Here's your graph: