We need to look at the before and after collisions of the pucks in order to find theta and the forces acting on the target in order to find the actual angle. We used the velocity vectors of each puck from the same time stamp in the x and y direction to find the angles before each collision, then used the formula theta = arccos((V1x*V2x)/(abs(V1*V2)). We multiplied the velocity in the x direction with the mass of the puck, 0.028 0.005 kg with the x velocity value we were looking at, to determine the x direction momentum before and after each collision. Next, for the y-velocity vectors, we also adopted the same method. And we repeated it for all eight of the collisions. We divided the moment from before the collision by the momentum after the collision to get the ratio in order to find the ratio of the x direction