Resolving Momentum

Momentum is a vector, so like any vector it can be split into two perpendicular components. Resolving momentum makes it possible to apply conservation of momentum to objects that move in different directions.An object of mass m moving with velocity v at an angle θ to the x-axis has momentum p = mv. Its component along the x-axis is mvcosθ and its component along the y-axis is mvsinθ.In a collision, momentum is conserved separately in each direction. The total momentum in the x direction before the collision equals the total momentum in the x direction afterwards, and the same is true in the y direction.When resolving, choose a positive direction for each axis. Components in the opposite direction are negative. Once the final x and y components are known, they can be combined with Pythagoras' theorem to find the size of the momentum and with tanθ to find its direction.