Animate
Start the applet. Blue moves in a circle at constant speed. At t=0, Blue releases a green ball. Note the path taken by the ball.
1. At t=0, suppose Blue throws the ball directly opposite his direction of motion. We'll call this 0 deg, measuring angles ccw from the +x axis. What must be the speed of the ball, relative to Blue, so that the ball does not move with respect to the grid?
2. Now Blue's problem (and yours) is to throw the ball with the right speed and angle so the ball intercepts Blue's path when Blue has moved through exactly one-half revolution.