SOLUTION: A rocket is shot into the air can be modeled by the equation y= -16x^2 + 420x + 250, where x represents the time the rocket is in the air and y represents the height of the rocke

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Question 1009309: A rocket is shot into the air can be modeled by the equation y= -16x^2 + 420x + 250, where x represents the time the rocket is in the air and y represents the
height of the rocket at the given time.
What is the initial height of the object?
What is the initial velocity of the object?
At what time does the rocket reach the ground?
At what time does the rocket reach its maximum height?
What is the maximum height achieved by the rocket?
At what time is the rocket at 200ft?
At what time is the rocket at 1500ft?
What is the height of the rocket at 3.75 seconds?

Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
A rocket is shot into the air can be modeled by the equation y= -16x^2 + 420x + 250, where x represents the time the rocket is in the air and y represents the
height of the rocket at the given time.
What is the initial height of the object?:: f(0) = 250 ft.
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What is the initial velocity of the object?:: 420 ft/sec
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At what time does the rocket reach the ground?
Solve:: -16x^2 + 420x + 250 = 0
x = 26.83 seconds
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At what time does the rocket reach its maximum height?
Ans:: when x = -b/(2a) = -420/(-2*-16) = 13.125 sec
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What is the maximum height achieved by the rocket?
Ans: f(13.125) = 3006.3 ft
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At what time is the rocket at 200ft?
Solve -16x^2 + 420x + 250 = 200
x = 26.37 sec
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At what time is the rocket at 1500ft?
Solve -16x^2 + 420x + 250 = 1500
x = 3.42 sec and x = 22.83 sec
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What is the height of the rocket at 3.75 seconds?
f(3.75) = 1600 ft
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Cheers,
Stan H.
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