Prove that bodies of identical masses exchange their velocities after head on collision - Physics - Work Energy And Power

Question

Prove that bodies of identical masses exchange their velocities
after head on collision

Trunaya · Accepted Answer

in elastic collision,
v2 - v1 = u1 -
u2
so v2 = u1 - u2 + v1
(1)
from coservation of linear momentum,
m1u1 + m2u2 =
m1v1 + m2v2
but since masses are equal,
mu1 + mu2 = mv1 + mv2
substituting the value for v2 from (1)
m(u1 + u2) = m(v1 +
u1 - u2 +v1)
mu1 + mu2 = 2mv1 +
mu1 - mu2
2mu2 = 2mv1
u2 = v1
substituting this value of v1 in (1) we get,
v2 = u1 - u2 +
u2
v2 = u1
as u can see, the initial velocity of one body has now become
the final velocity of second body after collision and
initial velocity of the second body has becum the final velocity
of the first

Prove that bodies of identical masses exchange their velocities after head on collision.