physics

The height of a certain waterfall is 33.2 m. When the water reaches the
bottom of the falls, its speed is 25.8 m/s. Neglecting air resistance, what is
the speed of the water at the top of the falls?

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  1. The speed is horizontal at the top, call it u
    and
    it remains u all the way down because there is no horizontal force (acceleration).

    So we have a vertical problem first.

    v = g t
    h = (1/2) g t^2
    so
    33.2 = 4.9 t^2
    t^2 = 6.77
    t = 2.60 seconds

    so v = 9.81 * 2.6 = 25.5 m/s down

    speed = s = 25.8 = sqrt(u^2 + 25.5^2)
    u^2 + 652 = 666
    u^2 = 13.64
    u = 3.69 m/s

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