# Special Cases of Head-on Elastic Collision

If projectile and target are of same mass, i.e. m1 = m2

Since

and .

Substituting m1 = m2, we get

v1 = u2 and v2 = u1

It means when two bodies of equal masses undergo head-on elastic collision, their velocities get interchanged.

Example

Collision of two billiard balls

Fig. 4

 Sub case: u2 = 0 i.e., target is at rest. Therefore, v1 = 0 and v2 = u1
If a massive projectile collides with a light target, i.e., m1 >> m2

Since

and

Substituting m2 = 0, we get
v1 = u1 and v2 = 2u1 â€“ u2

 Sub case: u2 = 0, i.e., target is at rest. Therefore, v1 = u1 and v2 = 2u1

If a light projectile collides with a very heavy target i.e. m1 << m2

Since

and .

Substituting m1 = 0, we get
v1 = â€“u1 + 2u2 and v2 = u2

Example

Collision of a ball with a massive wall.

Fig. 5

 Sub case: u2 = 0, i.e., target is at rest. Therefore, v1 = â€“ u1 and v2 = 0, i.e., the ball rebounds with same speed in opposite direction when it collides with stationary and very massive wall.