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28 October, 04:14

A baseball is hit nearly straight up into the air with a speed of 22 m/s. (a) how high does it go? (b) how long is it in the air? neglect air resistance.

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  1. 28 October, 04:19
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    Refer to the diagram shown below.

    When the ball attains maximum height, it will have zero vertical velocity.

    The maximum height, h. obeys the equation

    0 = (22 m/s) ² - 2 * (9.8 m/s²) * (h m)

    h = 22² / (2*9.8) = 24.694 m

    Answer: The maximum height attained is 24.7 m (nearest tenth)

    Part b.

    The vertical height traveled by the ball obeys the equation

    h = (22 m/s) t - (1/2) * (9.8 m/s²) * (t s) ²

    where

    h = vertical height, m

    g = 9.8 m/s², acceleration due to gravity

    t = time, s

    To find how long the ball stays in the air, set h = 0 to obtain

    4.9t² - 22t = 0

    t (4.9t - 22) = 0

    t = 0, or t = 22/4.9 = 4.49 s

    t = 0 corresponds to the launch, and t = 4.49 s corresponds to when the ball retuns to the ground.

    Answer: The ball stays in the air for 4.5 s (nearest tenth)
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