POSSIBLE SOLUTION(S)

First, a coordinate system: Place home plate at the origin and the field in the first quadrant. (That is, the first base line is the positive x-axis and the third base line is the positive y-axis.)

Now, let's define the lines/curves that give us the outfield fence.

We are told that the lowest part of the fence (that is, the fence at the point in the park at which it is hardest to get a home run) is to be 10 feet high. This will be at the point furthest from home plate. That point will be somewhere on the quarter circle.

How much initial velocity is necessary to hit the ball over a 10 foot fence d[xfar] feet from home plate? Assuming the simplest model for projectile motion (no wind resistance), parametric equations for the position of the ball are given by

We want to know for what value of V0 will there be some time when the distance traveled will be d[xfar] and the height be 10 feet.

Now, to find the proper height of the fence at each point, all we need to do is determine the distance of that point to the origin, and find the height of the ball at the time when the ball has traveled that distance with this initial velocity. For instance, at the (baseline) end of right field,

We can find the appropriate height of the fence at a distance d from home plate by defining

Changing the launch angle requires only a few small changes.

Let's plot this wall (using the 30 degree launch angle)