# 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.
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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 (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=7652 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: -0.54611596607863, 4.92111596607863. Here's your graph:

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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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