Two spheres A and B of mass m and 3m collide. Their initial velocities are 4u and -u respectively. Find the speeds of A and B after impact in terms of u and the coefficient of restitution e.

Let $m_A = m$ and $m_B = 3m$ be the masses of spheres A and B, respectively.
Let $u_A = 4u$ and $u_B = -u$ be their initial velocities (taking the direction of A as positive).
Let $v_A$ and $v_B$ be their velocities after impact.

i) Find in terms of $u$ and $e$ the speeds of A and B after impact.

Step 1: Apply the principle of conservation of momentum.

$$m_A u_A + m_B u_B = m_A v_A + m_B v_B$$