Question

prove that when two bodies of equal masses undergo elastic collision in one dimension,their velocities are just interchanged.

Answer 1

hope this is the right ans

Answer 2

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.