STATEMENT OF PROBLEM

A baseball park is 325 feet down the third base line and 425 feet down the first base line. The outfield fences are perpendicular to the baselines for a distance of 250 feet (left field) and 150 feet (right field). The remaining portion of the outfield fence is a quarter circle.

You have been asked to design the outfield fence so that the field does not favor hitters from one side of the plate.

1. If, at its lowest point, the fence must be exactly 10 feet high, how high should the fence be at all points along the outfield boundary? Assume a launch angle (the angle the ball makes with the horizontal as it comes off the bat) of 25 degrees. You should also assume -- at least for starters -- that the wind resistance is negligible so that the only force acting on the ball after it has been hit is due to gravity. Finally, assume the ball strikes the bat 3 feet above the ground.

2. How sensitive is the height of the fence to slight changes in the launch angle? What if the launch angle is 30 degrees?