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29 October, 05:23

A model rocket is launched vertically from a platform 64 feet above the ground. The height the rocket reaches during the flight is modeled by the equation s (t) = - 16t2 48t 64, where s is the height of the rocket and t is the time in seconds since the launch. After how many seconds will the rocket hit the ground?

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  1. 29 October, 08:41
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    At ground level, the height is = 0. Therefore, s (t) = 0.

    0 = - 16t2 + 48t + 64

    Divide both sides by - 16.

    0 = - 16 (t2 - 3t - 4)

    We are left with this equation: 0 = t2 - 3t - 4

    Factor out.

    0 = (t - 4) (t+1)

    We solve each separately.

    0 = (t-4)

    t = 4

    0 = (t+1)

    t = - 1

    We are left with two answers but time cannot be negative so t = 4 seconds.
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