Mathematics and baseball, math, Marketing Management

A baseball left fielder throws a baseball from a position 400 feet from home plate to the third baseman who is 90 feet from home plate. (Assume the two players are in the same line from home plate.) The throw is made at a speed of 90 miles per hour at an angle of 20o. (Be careful with units here.) Special Note: Assume the outfielder is 6 feet tall and that the initial throw starts at about 6 feet above ground. Assume, for simplicity, there is no air resistance.
a) Will a third baseman who is 6 feet tall be able to catch the ball on the fly? (Keep in mind that the third baseman can catch a ball in the air if the ball is at any height between 0 and some reasonable distance above his head.) How long will it take the ball to get to the third baseman?
b) Answer Part a) if the initial speed is 80 miles per hour with the same initial angle.
c) Answer Part a) if the initial speed is 90 miles per hour but the initial angle is only 10o.
d) Investigate various combinations of initial velocity and initial angle from the outfielder so that the third baseman can catch the ball on the fly.
e) To help with part f), fix the initial speed and vary the throwing angle; then fix the throwing angle and vary the initial speed. What effects do you observe for various angles with the same speed? What effects do you observe for various speeds with the same throwing angle?
f) Write a short essay describing the left fielder’s best strategy in terms of initial angle and initial velocity in order to get the ball to the third baseman on the fly.

Suggestions:
a) Convert velocities from mph to feet per second since the height and vertical distances are in feet.
b) Convert all angle measures to radians.
c) Sketch the graph for various values of the angle ? and initial velocity v0. Observe the height, y at the location of the third baseman.

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