Question 395290: A model rocket is launced into the air and follows a parabolic path described by the function h(t)=-5t^2 + 40t +2, where t is time in seconds after the rocket is launched and h(t) is the height of the rocket above the ground in metres. Algebraically determine the maximum height reached by the rocket and the time it takes the rocket to reach it's maximum height.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! A model rocket is launced into the air and follows a parabolic path described by the function h(t)=-5t^2 + 40t +2, where t is time in seconds after the rocket is launched and h(t) is the height of the rocket above the ground in metres. Algebraically determine the maximum height reached by the rocket and the time it takes the rocket to reach it's maximum height.
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h(t)=-5t^2 + 40t +2
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Max occurs when t = -b/(2a) = -40/(2*-5) = 4 seconds
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Max height = h(4) = -5(4^2)+40(4)+2 = 82 meters
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Cheers,
Stan H.
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