physic

A golfer hits his approach shot at an angle of
θ = 52.8°,
giving the ball an initial speed of
v0 = 37.0 m/s
(see figure below). The ball lands on the elevated green,
yf = 5.3 m
above the initial position near the hole, and stops immediately.

(a) How much time passed while the ball was in the air?

s

(b) How far did the ball travel horizontally before landing?

m

(c) What was the peak height reached by the ball?

m

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  1. vyi = 37.0 sin52,8° = 29.47 m/s
    vix = 37.0 cos52.8° = 22.37 m/s

    (a) the ball's height y is
    y(t) = 29.47t - 4.9t^2
    So, when it hits the green,
    29.47t - 4.9t^2 = 5.3
    t = 5.829

    (b) the horizontal distance, at constant speed is

    x = 5.829 * 22.37 = 130.39

    (c) the vertex of the parabola is at
    t = -b/2a = 29.47/9.8 = 3.01
    y(3.007) = 44.31

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