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Special Cases of Head-on Elastic Collision

If projectile and target are of same mass, i.e. m1 = m2
Since 42405.png
and 42398.png.
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.

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 42451.png
and 42444.png
Substituting m2 = 0, we get
v1 = u1 and v2 = 2u1 – 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 42499.png
and 42493.png.
Substituting m1 = 0, we get
v1 = –u1 + 2u2 and v2 = u2

Collision of a ball with a massive wall.




Fig. 5


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

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