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11 May, 00:12

A baseball hit just above the ground leaves the bat 27 m/s at 45° above the horizontal. A) How far away does the ball strike the ground? B) What is the maximum height of the ball?

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  1. 11 May, 00:32
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    A) The ball hits the ground 74.45 m far from the hitting position.

    B) Maximum height of the ball = 18.57 m

    Explanation:

    There are two types of motion in this horizontal and vertical motion.

    We have velocity = 27 m/s at 45° above the horizontal

    Horizontal velocity = 27cos45 = 19.09 m/s

    Vertical velocity = 27sin45 = 19.09 m/s

    Time to reach maximum height,

    v = u + at

    0 = 19.09 - 9.81 t

    t = 1.95 s

    So total time of flight = 2 x 1.95 = 3.90 s

    A) So the ball travels at 19.09 m/s for 3.90 seconds.

    Horizontal distance traveled = 19.09 x 3.90 = 74.45 m

    So the ball hits the ground 74.45 m far from the hitting position.

    B) We have vertical displacement

    S = ut + 0.5 at²

    H = 19.09 x 1.95 - 0.5 x 9.81 x 1.95² = 18.57 m

    Maximum height of the ball = 18.57 m
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