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This result may in like manner be generalised. Retaining the former symbols, the moving forces of A and B before impact will be A × a and B × b and their forces after impact will be A × x and B × x. The force lost by A will therefore be A × a - A × x. The mass B will have lost all the force B × b which it had in its former direction, and will have received the force B × x in the opposite direction. Therefore the actual force imparted to B by the collision will be B × b + B × x. But since the force lost by A must be equal to that imparted to B, we shall have

A × a - A × x = B × b + B × x

and therefore

(A + B)×x = A × a - B × b

and if the common velocity after impact be required, we have

x = A × a - B × b/A + B

As a general rule, therefore, to find the common velocity after impact. Multiply the weights by the previous velocities and take their sum if the bodies move in the same direction, and their difference if they move in opposite directions, and divide the one or the other by the sum of their weights. The greatest will be the velocity after impact.