Physics

posted by Raye

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?

  1. Damon

    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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