Explain with neat sketch 1) Direct central Impact 2) Oblique central Impact.

Line of impact: the common normal to the surfaces of the two colliding bodies at the point of contact. If the mass centres of both bodies lie on this line, the impact is central.

1) Direct central impact: the line of impact passes through both mass centres and the velocities of both bodies before impact are directed along the line of impact.

   u1 -->        <-- u2
   ( A )  ------  ( B )      line of impact (through both centres)
   after: v1 , v2 along the same line

Equations: momentum \(m_1u_1 + m_2u_2 = m_1v_1 + m_2v_2\); coefficient of restitution \(e = \dfrac{v_2 - v_1}{u_1 - u_2}\). Example: two billiard balls moving along the line joining their centres.

2) Oblique central impact: the line of impact passes through both mass centres, but the velocity of one or both bodies is inclined to the line of impact.

        u1 (at angle a1)           u2 (at angle a2)
          \                          /
           ( A ) ------ n ------ ( B )     n = line of impact
                   t (tangent, perpendicular to n)

Velocities are resolved along the line of impact (n) and the common tangent (t). Along t: components of each body remain unchanged (no impulsive force along t). Along n: total momentum is conserved and \(e = \dfrac{v_{2n} - v_{1n}}{u_{1n} - u_{2n}}\). Example: a ball striking another ball at an angle, or a ball hitting a wall obliquely.