State what the principle of conservation of momentum says.
Two balls, X and Y, travel across a horizontal frictionless surface, as shown from above in Fig. 4.1. Ball X has a mass of $3.0\,\text{kg}$ and a velocity of $4.0\,\text{m s}^{-1}$ in a direction at angle $\theta$ to line AB. Ball Y has a mass of $2.5\,\text{kg}$ and a velocity of $4.8\,\text{m s}^{-1}$ in a direction at angle $\theta$ to the line AB. The balls collide and stick together. After the collision, the balls move at a velocity of $3.7\,\text{m s}^{-1}$ along line AB on the horizontal surface, as shown in Fig. 4.2. By considering the components of the momentum along line AB, calculate $\theta$.
From the kinetic energies, state and explain whether the collision of the balls is inelastic or perfectly elastic.