I'm wondering about how to calculate the resultant velocity vectors of an elastic collision of two particles of same mass, in 3d. I've seen a post on the subject in which you answered, but I didn't quite get it... I know you have to calculate the velocity and direction of the normal vector but I'm not sure how to do it.
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1Possible duplicate of Determine resultant velocity of an elastic particle-particle collision in 3d space. Please see my answer on that page – Mar 02 '16 at 19:40
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Edit: (I had assumed the asker had too much prior knowledge)
Okay, so in any collision momentum is conserved. This means that $$m_1\vec{v}_1+m_2 \vec{v}_2=m_1 \vec{v}_1'+m_2\vec{v}_2'$$ Where $\vec{v}_i$ is the initial velocity of particle i and $\vec{v}_i'$ is the final velocity of particle i.
Furthermore, by definition, for an elastic collision the kinetic energy is conserved, so $$\frac{1}{2}m_1 v_1^2 + \frac{1}{2}m_2 v_2^2 = \frac{1}{2}m_1 v_1'^2 + \frac{1}{2}m_2 v_2'^2 $$
Using these two equations, you can find the final velocities given the initial velocities.
