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27 April, 03:30

A batter hits a fly ball which leaves the bat 0.89 m above the ground at an angle of 62 ∘ with an initial speed of 29 m/s heading toward centerfield. Ignore air resistance. How far from home plate would the ball land if not caught? The ball is caught by the centerfielder who, starting at a distance of 107 m from home plate, runs straight toward home plate at a constant speed and makes the catch at ground level. Find his speed.

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  1. 27 April, 06:57
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    consider the motion in Y-direction

    v₀ = initial velocity = 29 Sin62 = 25.6 m/s

    a = acceleration = - 9.8 m/s²

    t = time of travel

    Y = vertical displacement = - 0.89 m

    using the equation

    Y = v₀ t + (0.5) a t²

    - 0.89 = (25.6) t + (0.5) ( - 9.8) t²

    t = 5.3 sec

    consider the motion along the horizontal direction:

    v₀ = initial velocity = 29 Cos62 = 13.6 m/s

    a = acceleration = 0 m/s²

    t = time of travel = 5.3 sec

    X = horizontal displacement = ?

    using the equation

    X = v₀ t + (0.5) a t²

    X = (13.6) (5.3) + (0.5) (0) t²

    X = 72.1 m

    d = distance traveled by the center fielder to catch the ball = 107 - x = 107 - 72.1 = 34.9 m

    t = time taken = 5.3 sec

    v = speed of center fielder

    using the equation

    v = d/t

    v = 34.9/5.3

    v = 6.6 m/s
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