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The height, h(t), of a baseball, in metres, at time t seconds after it is tossed out of a window is modelled by the function h(t) = -5t^2 + 20t + 15. A boy shoots at the baseball with a paintball gun. The
trajectory of the paintball is given by the function g(t) = 3t + 3. Will the paintball hit the baseball? If so, when? At what height will the baseball be?

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  1. You'll be solving
    -5t^2 + 20t + 15 = 3t + 3
    5t^2 - 17t - 12 = 0
    (t - 4)(5t + 3) = 0
    t = 4 or t = -3/5, but let's assume t ≥ 0

    They will hit after 4 seconds,

    to find the height, sub t = 4 into h(t)

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