Physics

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A baseball is hit by Aaron Judge, a New York Yankees baseball team member, at an amazing velocity of 110 miles/hour at an angle of 35 degrees from the horizontal from home plate in Yankee Stadium in New York City. The baseball was initially launched from an elevation of 4 feet above ground. The distance from home plate to the outfield wall is 408 feet at center field. The height of the outfield wall is approximately 8 feet (It varies slightly across the outfield). You should first draw a two-dimensional picture of the baseball’s trajectory (x, y coordinate system) to assist in developing answers to the questions below. Note: Convert all variables to the metric (mks) system before performing your calculations.
b)What is the maximum height reached by the ball?
c)What is the total time of flight?

  • Physics -

    No I will not use miles and feet
    49.2 meters/sec = 110 mph
    u = horizontal speed = 49.2 cos 35 = 40.3 m/s
    that is constant
    so
    x = 40.3 t

    vertical problem:
    v = Vi - 9.81 t
    Vi = 49.2 sin 35 deg = 28.2 m/s
    so
    v = 28.2 -9.81 t
    at top, v = 0
    so t = 2.87 seconds to top

    h = top = Hi + Vi t - 4.9 t^2
    Hi = 4 feet = 1.22 meters
    h = 1.22 + 28.2(2.87)-4.9(2.87)^2
    h = 1.22 + 80.9 - 40.4
    = 41.7 meters at top

    when does it reach 8 feet?
    2.44 = 1.22 + 28.2 t -4.9 t^2
    solve quadratic for t

    use range = u*t to see if it cleared the wall
    if it did solve for t at h = 0

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