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calculus 3

A golf ball is driven down a horizontal fairway with an initial speed of 55m/s at an initial angle of 25 degrees. (Assume the tee from which the ball is hit is of negligible height).
a). how far does the ball travel horizontally b). when does the ball land? c). what is the max height? d). at what angle should the ball be hit to reach a green 300m from the tee?

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  1. the vertical speed of the ball is 55 sin 25° = 23.24 m/s

    So, the height y is

    y = 23.24t - 16t^2

    The horizontal speed is a constant 49.85 m/s

    (b,a) find when y=0
    x = 49.85t

    (c) max height at the vertex of the parabola

    (d) assuming the same 55 m/s initial speed,
    find t when x=300
    use that t to find v in

    vt-16t^2 = 300
    then sinθ = v/55

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