(100 points) Crazy Hockey:

After retiring from his successful ice hockey career as an enforcer, Doug Glatt wants to open the first crazy hockey course. His idea is to create a game like miniature golf - where instead of putting a ball into holes, you are slap shooting a puck into small goals. He has heard a lot of positive word-of-mouth about your work on the tv show “Holey Moley” and would like you to design one of the goals. He is not sure about the theme of the goal, but he demands that the goal be accessible via two separate paths. In other words, there need to be two different ways to score the same goal. One path must involve the puck leaving the ground by at least 5 meters (essentially jumping over a vent that is forcing area across the course) and the other must involve the puck going through an area of forced air coming from a vent that is blowing at 4 m/s perpendicular to the path of the puck if the puck was hit straight from the starting point. The area that the forced air blows across must be one meter long. Doug wants to see the physics behind your design and predictions as evidence that the shots can be made but tells you to have fun with it.

A good solution is not just equations and numeric predictions but will include commentary and discussion of those equations and predictions and reflections on what those predictions mean. We encourage you to use the simplest model that correctly captures the essential physics.