A projectile is fired from a cliff 300 m high with an initial velocity of 400 m/s. If the firing angle is 30 degrees from the horizontal, compute the horizontal range of the projectile.

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  1. Horizontal problem:
    u = 400 cos 30 forever
    range = u t
    where t is the time from the vertical problem

    Vertical problem:
    Hi = 300 meters
    Vi = 400 sin 30 = 200 m/s
    v = Vi - 9.81 t
    h = Hi + Vi t - 4.9 t^2
    0 = 300 + 200 t - 4.9 t^2
    solve that quadratic for t (the positive root, not the one that occurs inside the virtual cliff on the way up)
    Use that time in the air in the horizontal problem to get range.

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