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## Homework Statement

A very massive object with a velocity "v" collides head-on with an object at rest whose mass is very small. no kinetic energy is converted into other forms. Prove that the low-mass object recoils with a velocity 2"v"

use the center-of-mass frame of reference.

## Homework Equations

p=mv

ke= 1/2mv^2

M1>m2

## The Attempt at a Solution

my book doesn't actually describe the center of mass frame of reference so I'm lost there. But trying to solve for it:

m1*v1=m1*v2+m2*2*v1

m1(v1-v2)= m2*2*v1

(v1-v2)m1/m2=2*v1

conservation of momentum

m1*v1 + m2*0= m1*v2+ m2*2*v1

m1*v1 = m1*v2+ m2*2*v1

m1*v1 - m2*2*v1 = m1*v2

v1(m1 - m2*2)/m1 = v2

conservation of energy

1/2*m1*(v1)^2 +1/2*m*0= 1/2*m1*(v2)^2 +1/2*m2*(2v1)^2

1/2*m1*(v1)^2 = 1/2*m1*(v2)^2 +1/2*m2*(2v1)^2

1/2*m1*(v1)^2 = 1/2*m1*(v1(m1 - m2*2)/m1)^2 +1/2*m2*(2v1)^2

m1*(v1)^2 = m1*(v1(m1 - m2*2)/m1)^2 +m2*(2v1)^2

0 = m1*(v1(m1 - m2*2)/m1)^2 +m2*(2v1)^2 - m1*(v1)^2