09-11 Collisions in Two Dimensions

For a collision in two dimensions (a glancing collision), momentum is conserved both in the X and the Y directions.  If the struck object is initially at rest and we let the direction of travel of the striking object be the X direction, then the sum of the Y momenta after the collision will be zero since there was no Y momentum to begin with.  Likewise the sum of the X momenta after the collision will be equal to the original momentum of the striking object.

Section 9-11 does not go into a lot of detail about glancing elastic collisions (not head-on).  The book mentions (on p.224 above Checkpoint 9) that a system of equations with seven variables, four of which are known, can be solved using three equations - conservation of momentum in the x, conservation of momentum in the y, and conservation of kinetic energy.  More detail is given below in the files labeled Elastic Collision in 2D.  A Java simulation of this collision can be found here.   Also choose e=1 in the simulation's menu for an elastic collision.

Excel spreadsheet for calculations used in simulation