Elastic Collision in Two Dimensions (Oblique Collision)

If the colliding bodies do not move along the same straight line path, then the collision is said to be an oblique collision.

A body of mass m₁ is moving with a velocity along X-axis. Let it suffer elastic collision with a stationary body of mass m₂. The distance b, between the initial line of motion and a line parallel to it through the centre of the target body is called the impact parameter. This is a measure of the directness of the collision. It may be defined as the distance by which the collision misses being head-on.

Clearly, for a head-on collision, b = 0.

After collision, let body of mass m₁ be deflected at angle q₁ with the initial direction. The body of mass m₂ is deflected at angle q₂ with the initial direction.

Let  be the velocities of bodies of masses m₁ and m₂ respectively, after the collision.

Applying the law of conservation of momentum to the X-component of motion, we get

For Y - component of motion,

The collision is elastic. So kinetic energy will be conserved.

In the equations (1), (2) and (3) v_1f and v_2f can be resolved_, if m₁, m₂, v_1f, v_2f, q₁ and q₂ are known.