State the principle that momentum is conserved.
Ball A has speed $v$ and moves on a horizontal frictionless surface towards ball B at rest, as shown in Fig. $3.1$. Ball A has mass $4.0\,\text{kg}$ and ball B has mass $12\,\text{kg}$. After they collide, the balls separate as shown in Fig. $3.2$. Ball A then has velocity $6.0\,\text{m s}^{-1}$ at an angle of $\theta$ to its original direction of travel. Ball B then has velocity $3.5\,\text{m s}^{-1}$ at an angle of $30^\circ$ to the original direction of motion of ball A.
Using the momentum components at right angles to the initial path of ball A, calculate $\theta$.
Use your answer in (i) to show that the initial speed $v$ of ball A is $12\,\text{m s}^{-1}$. Give your working.
Using calculations of kinetic energy, state and explain whether the collision is elastic or inelastic.