The October, 2008 PoW

It is well known that a ball thrown at a fixed speed along a flat field will travel farthest if it is thrown at an angle of 45 degrees. (The ball is thrown and caught at the same height, and we neglect air resistance. )

flat
The above shows the path of a ball with initial speed 66ft/sec. thrown and caught at a height of 5 ft.
Also, I take g = -32ft/sec2, but that doesn't factor into A.

Find the angle A at which the ball will travel farthest if it is thrown down a hill that is at a constant angle B with a horizontal.

flat
The above shows the path of a ball with initial speed 66ft/sec. thrown down a hill with B = p/8 = 22.5 degrees.

Also find the angle A at which the ball will travel farthest if it is thrown up a hill that is at a constant angle of B with a horizontal.

flat
The above shows the path of a ball with initial speed 66ft/sec. thrown up a hill with B = p/8 = 22.5 degrees.