The principle of conservation of momentum applies in two dimensions as well as one. In a closed system, the total momentum before a collision equals the total momentum after it, both in size and in direction.To solve a two-dimensional collision, resolve every momentum into components along two perpendicular axes, usually along and at right angles to the original direction of motion. Then write one conservation equation for each axis.Consider a ball A of mass m moving at speed u along the x-axis. It strikes a stationary ball B of equal mass, and the two balls move off at speeds vA and vB at angles α and β either side of the x-axis. Along x: mu = mvAcosα + mvBcosβ. Along y: 0 = mvAsinα - mvBsinβ.The y equation shows that the two y-components must be equal and opposite, because there was no momentum in the y direction to begin with. Given the angles and one final speed, the two equations can be solved for the unknowns.
The problem can also be solved with a vector triangle: the initial momentum is the vector sum of the two final momenta, so the three vectors form a closed triangle when drawn tip to tail. If the collision between equal masses is perfectly elastic and one ball is initially at rest, the two balls always move off at 90° to each other.
The problem can also be solved with a vector triangle: the initial momentum is the vector sum of the two final momenta, so the three vectors form a closed triangle when drawn tip to tail. If the collision between equal masses is perfectly elastic and one ball is initially at rest, the two balls always move off at 90° to each other.