Two smooth spheres. `A` and `B`. having equal radii, lie on a horizontal table. `A` is of mass `m` and `B` is of mass `3m`. The spheres are projected towards each other with velocity vector `5hati+2hatj` and `2hati-hatj`, respectively, and when they collide the lige joining their centres is parallel to the vector `hati`. If the coefficient of restitution between `A` and `B` is `1//3`, find the velocities after impact and the loss in kinetic energy caused by the collision. Find also the magnitude of the impulses that act at the instant of impact.

Explanation

To solve the problem step by step, we will follow the principles of conservation of momentum and the coefficient of restitution.

### Step 1: Identify the initial velocities and masses
- Mass of sphere A, \( m_1 = m \)
- Mass of sphere B, \( m_2 = 3m \)
- Initial velocity of sphere A, \( \vec{u_1} = 5\hat{i} + 2\hat{j} \)
- Initial velocity of sphere B, \( \vec{u_2} = 2\hat{i} - \hat{j} \)

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