SOLUTION: If a model rocket is launched with a trajectory of h(t) = -16t^2+96t+112 (where t = time in seconds), what is the maximum height the rocket reaches? When does it hit the ground?

Question 1055228: If a model rocket is launched with a trajectory of h(t) = -16t^2+96t+112 (where t = time in seconds), what is the maximum height the rocket reaches? When does it hit the ground?

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
If a model rocket is launched with a trajectory of h(t) = -16t^2+96t+112 (where t = time in seconds),
what is the maximum height the rocket reaches? When does it hit the ground?
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Height is zero when the rocket hits the ground.
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-16t^2 + 96t + 112 = 0
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t^2 - 6t - 7 = 0
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(t-7)(t+1) = 0
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The rocket hits the ground at t = 7 seconds
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The max height occurs when t = -b/(2a) = -96/((-2)*16) = 3 sec
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That max height = f(3) = -16*3^2 + 96*3 + 112 = 256 ft
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Cheers,
Stan H
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