Two physics students built a model rocket for a class project. Once the rocket is launched, its height in feet, h(t), can be found using the function h(t) = -16t² + 96t, where t represents time in seconds.

The height if the rocket at t = 5 is given by h(5) = -16*5^2 + 96*5 = -16*25 + 96*5 = 80.

The height of the rocket is equal to 80 at the time t where. Solving the quadratic equation gives:

16*t^2 - 96t = -80

=> t^2 - 6t + 5 = 0

=> t^2 - 5t - t + 5 = 0

=> t(t - 5) - 1(t - 5) = 0

=> (t - 1)(t - 5) = 0

=> t = 1 and t = 5

The rocket is at a height of 80 at t = 1 and t = 5

The path followed by the rocket is that of a parabola. It is at a height of 80 first while going up and then again while coming down.

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