A rocket is launched from atop a 75 foot cliff with an initial vertical velocity of 107 feet per second. The height of the rocket t seconds after launch is given by the equation h = - 16t + 107t + 75. Graph the equation to find out how long after the rocket is launched it will hit the ground. Estimate your answer to the nearest tenth of a second.

Question

Mathematics

Bridgett

5 September, 06:49

A rocket is launched from atop a 75 foot cliff with an initial vertical velocity of 107 feet per second. The height of the rocket t seconds after launch is given by the equation h = - 16t + 107t + 75. Graph the equation to find out how long after the rocket is launched it will hit the ground. Estimate your answer to the nearest tenth of a second.

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Answers (1)

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Joselyn Mendoza · Answer 1

The distance of the rocket hitting the ground is 715.56 feet in 6.68 seconds

Explanation:

Given:

Height, h = 75 foot

Initial velocity, u = 107 foot/sec

Equation:

h = - 16t² + 107t + 75

Substituting the equation:

75 = - 16t² + 107t + 75

0 = - 16t² + 107t

16t² = 107t

t = 6.6875s

We know:

Distance = speed X time

d = 107 f/s X 6.6875s

d = 715.56 foot

Therefore, the distance of the rocket hitting the ground is 715.56 feet in 6.68 seconds