(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A particle with mass m and speed v collides with another particle with

mass m, which is initially stationary. The collision is elastic. Show that

the particles travel in perpendicular directions after the collision.

2. Relevant equations

1)initial momentum = final momentum

2)initial kinetic energy = final kinetic energy

3. The attempt at a solution

Assume that B is the moving particle and A is the stationary particle.

By conservation of momentum,

For the horizontal component of the motion

mv_{i}=mv_{f}cos[tex]\theta[/tex]+mu_{f}cos[tex]\phi[/tex]

For the vertical component of the motion

0=mv_{f}sin[tex]\theta[/tex]+mu_{f}sin[tex]\phi[/tex]

where

v_{i}= initial velocity of B

v_{f}= final velocity of B

u_{f}= final velocity of B

[tex]\theta[/tex] = angle between vector A and horizontal axis

[tex]\phi[/tex] = angle between vector B and horizontal axis

By conservation of energy,

[tex]\frac{1}{2}[/tex]mv_{i}^{2}=[tex]\frac{1}{2}[/tex]m(v_{f}^{2}+u_{f}^{2})

So, v_{i}^{2}=v_{f}^{2}+u_{f}^{2}

These are all the equations (3 equations 5 variables) I can get,

But it seems that I have too many variable so I cant solve for [tex]\theta[/tex] and [tex]\phi[/tex]. Is there any more assumption I need to make in order to solve the question?

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# Homework Help: Conservation of Momentum (Elastic Collision)

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