A ball is thrown horizontally from a height of 17.7 m and hits the ground with a speed that is 3.00 times its initial speed. What is the spe

Question

A ball is thrown horizontally from a height of 17.7 m and hits the ground with a speed that is 3.00 times its initial speed. What is the speed in the vertical direction just before the ball hits the ground

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Dulcie 5 years 2021-08-25T09:31:27+00:00 1 Answers 36 views 0

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  1. Nho
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    2021-08-25T09:32:57+00:00
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    Answer:

    19.76 m/s

    Explanation:

    Let v be the speed just before the ball hits the ground. The v/3 is the initial speed. When the ball falls to the ground its potential energy is converted to kinetic energy: E_p + E_{k0} = E_k[tex]mgh + mv_0^2/2 = mv^2/2[/tex]where m is the mass and h = 17.7 is the vertical distance traveled, v_0 = v/3 is the initial velocity , and g = 9.81 m/s2 is the gravitational acceleration. We can divide both sides by m:

    gh + v^2/18 = v^2/2

    gh = 9v^2/18 - v^2/18 = 8v^2/18 = 4v^2/9

    9.81*17.7 = 4v^2/9

    v^2 = 390.68

    v = \sqrt{390.68} = 19.76m/s

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