SOLUTION: A rocket on a computer screen has a path modeled by the equation h=-t2+3t+10 where t is time in seconds and h is the height above a platform and is in computer units. Find how long
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-> SOLUTION: A rocket on a computer screen has a path modeled by the equation h=-t2+3t+10 where t is time in seconds and h is the height above a platform and is in computer units. Find how long
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Question 1062615: A rocket on a computer screen has a path modeled by the equation h=-t2+3t+10 where t is time in seconds and h is the height above a platform and is in computer units. Find how long the rocket takes to reach the platform.
Thank you. I would like to know how to obtain the answer. as well as the correct answer if you please.
I sincerely appreciate your assistance. Answer by rothauserc(4718) (Show Source):
You can put this solution on YOUR website! 1) h(t) = -t^2 +3t +10
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The graph of h(t) is a parabola that curves downward
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at t = 0, h(t) = 10, I assume this is the height of the platform above the ground
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The max height of the rocket is determined from the first derivative
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dh/dt = -2t + 3
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-2t + 3 = 0
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t = 3/2 = 1.5 seconds
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substitute for t in h(t)
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h(1.5) = -(1.5)^2 +3(1.5) + 10 = 12.25
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here is a graph of the parabola
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the rocket reaches the platform when
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x^2 = 3x
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x = 3
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to check this, substitute in equation 1)
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h(3) = -(3^2) +3(3) + 10 = 10
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the rocket reaches the platform when t = 3 seconds
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