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## Homework Statement

A particle of mass ##m_1## experienced a perfectly elastic collision with a stationary particle of mass ##m_2##. What fraction of the kinetic energy does the striking particle lose, if it recoils at right angles to its original motion direction.

(Ans: ##2m_1/(m_1+m_2)## )

## Homework Equations

## The Attempt at a Solution

Let the initial velocity of ##m_1## be ##v## and let the x-axis be along the initial direction of motion. After collision, the first particle flies off at right angles and let that direction be y-axis. The vertical component of velocity of ##m_2## after collision has the direction opposite to that of ##m_1##. Conserving momentum in x direction:

$$m_1v=m_2v_{2x}$$

Conserving momentum in y direction:

$$m_1v_1=m_2v_{2y}$$

where ##v_1## is the final velocity of ##m_1##. I still need one more equation.

Any help is appreciated. Thanks!