Imagine you have an object of, say, 5kg moving in the positive x direction at 2m/s. So it has 10kgm/s of momentum. Now imagine an elastic collision from the y direction that gives the object another 10m/s in the positive y direction. Therefore its momentum doubles. Now we know that the object has 10kgm/s in the x direction and 10m/s in the y direction. So then how does the object have only sqrt((100m/s)^2+(100m/s)^2), roughly 14.1kgm/s of momentum instead of 20kgm/s. Where did the momentum go?