Question

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. (a)a. Assuming no wind resistance, would the baseball go over outfield the wall for a home run? Would it land short of the wall? Would it hit the wall? Note: You must first convert all distances (in feet) from the British system into the metric system (in meters).

Answer 1

Vo = 110mi/h * 1600m/mi * 1h/3600s = 48.89m/s[35o]. = Initial velocity.
Xo = 48.89*Cos35 = 40.0 m/s. = Hor.
Yo = 48.89*sin35 = 28.0 m/s. = Ver.

4ft * 1m/3.3ft = 1.21 m.
8ft = 2.42 m.
408ft * 1m/3.3ft = 123.6 m.

Y = Yo + g+Tr = 0.
28 - 9.8Tr = 0
Tr = 2.86 s. = Rise time or time to reach max ht.

hmax = ho + Yo*Tr + 0.5g*(Tr)^2.
hmax = 1.21 + 28*2.86 - 4.9*(2.86)^2 = 41.2 m. = Max ht.

d = 0.5g*(Tf)^2 = 41.2-2.42.
4.9(Tf)^2 = 38.79
Tf = 2.81 s. = Fall time from max ht. to top of fence.

Range = Xo*(Tr+Tf) = 40*(2.86+2.81) = 218.8 m.

The range is greater than the distance from home plate to the center field wall(123.6m). Therefore, it's a home run!!