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5 July, 15:27

Ken Griffey Jr hits a baseball so that it leaves the bat with an initial speed of 37 m/s at an angle of 53.1 degrees above horizontal. When the ball is hit, it is 1.07 m above the ground. How much total time is does the ball spend in the air before hitting the ground? What is the maximum height of the ball relative to the ground? How far does the ball travel?

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  1. 5 July, 17:24
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    h = Vy t - 1/2 g t^2 = - 1.07 m final height of ball relative to being hit

    Vy = 37 * sin 53.1 = 29.6 m/s initial vertical velocity

    h = 29.6 t - 9.8 / 2 t^2

    4.9 t^2 - 29.6 t - 1.07 = 0

    Solving the quadratic for t = 6.08 sec for time of flight

    Vy - g t = 0 where t is time to reach max height

    t = 29.6 / 9.8 = 3.02 sec to reach max height

    S = Vx * t where t is the distance traveled

    S = V0 cos 53.1 * 6.08 = 37 *.60 * 6.08 = 135 m about 443 ft
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