Well there is this one game that we did back in my school. We had students put into groups. Every group was given some masking tape, plastic straws, paper and a ping pong ball. The objective of the game was to design a roller coaster that would cause the ball to reach the ground in the longest...
Hi,
Perhaps you could try to divide the forces F2 and F1 in the x and y directions.
Such that F2x = F2cos(A2), F2y = F2sin(A2), F1x = F1cos(A1), and F1y = F1sin(A1).
Hence, Your free body diagram would look a little like the attached picture.
Hope this answers your question!