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Old Oct 3rd 2017, 08:37 AM   #1
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Join Date: Sep 2017
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I need help with this problem.
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 baseballís 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.
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).
b. What is the maximum height reached by the ball?
c. What is the total time of flight? Note: If the ball goes over the outfield wall or lands short of the wall, you can assume the final elevation at impact is zero. If the ball hits the outfield wall (elevation is less than 8 feet when the ball is exactly 408 feet from home plate) then the time of flight will be different.
d. Provide a plot (drawing), using graph paper, of the vertical position of the ball as a function of the horizontal position of the ball. Assume the ball is hit down the middle of center field toward the outfield wall. Plot the vertical position every five meters traveled in the horizontal direction. Indicate the vertical position next to the points plotted. You should plot the position data with greater detail (resolution) near the outfield wall, if necessary. Also, for each vertical position point plotted, plot the associated time, in seconds, next to the vertical position.
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Old Oct 3rd 2017, 06:34 PM   #2
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Join Date: Aug 2008
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Have you performed the conversions as directed?

(a) use the equations $\Delta x = v_0 \cos{\theta} \cdot t$ to determine the time to reach the center field wall, then the equation $\Delta y = v_0 \sin{\theta} \cdot t - \dfrac{1}{2}gt^2$ to determine if the ball clears the wall.

(b) maximum height occurs when the y-component of velocity equals zero ...
$0 = v_0 \sin{\theta} - gt$, solve for $t$, then use the $\Delta y$ equation to determine the max height.

(c) set $\Delta y = -4 \, ft$ and solve for $t$
(remember to convert feet to meters first)

(d) get some graph paper and do as instructed ... you can eliminate the parameter of time to get $y$ as a function of $x$.
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