Derive the formulae for the ?nal velocties vf of two bodies with masses m1 and m

Question

Derive the formulae for the ?nal velocties vf of two bodies with masses m1 and m2 after a one dimensional, ideal elastic collision, if body 2 was at rest before the collision and body 1 was moving with velocity vi1.

Start with momentum conservation
m1 * vi1 = m1* vf1 + m2* vf2
and kinetic energy conservation
1/2 m1 (v1,i)^2 = 1/2 m1 (v1,f)^2 + 1/2 m2 (v2,f)^2
. . .
. . . show all intermediate steps please
. . .
vf1 = [(m1 - m2)/ (m1 + m2)] vi1 ; vf2 = [(2 m1)/(m1 + m2)] vi1

Explanation / Answer

v2 - v1 = u1 - u2----->(1) Also m1u1 + m2u2 = m1v1 + m2v2------>(2) Solve these two equations and you will get the required values. [[[[instead of using conservation of kinetic energies.Use the proprty of coefficient of restitution e = (v2-v1)/(u1-u2) )and for perfectly elastic collision e=1 ]]]]

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