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# Elastic collision - Part 1 - Hypotheses

## Hypotheses

In the following, assumption is made that the total kinetic energy of the two bodies after the impact is equal to their total kinetic energy before the collision. Consider two bodies, denoted by subscripts 1 and 2. Let :

• $$m_1$$, $$m_2$$ be the masses;
• $$\vec{u_1}$$, $$\vec{u_2}$$ the velocities before collision;
• $$\vec{v_1}$$, $$\vec{v_2}$$ the velocities after collision;
• ($$x_1$$,$$y_1$$) and ($$x_2$$,$$y_2$$) the coordinates of the bodies's center when the collision occurs.

This article deals with the computation of $$\vec{v_1}$$ and $$\vec{v_2}$$ according to $$m_1$$, $$\vec{u_1}$$, $$m_2$$, $$\vec{u_2}$$, $$x_1$$, $$y_1$$, $$x_2$$ and $$y_2$$.