Why isn't momentum conserved in this elastic collision?

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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?
 

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Orodruin
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Momentum is a vector quantity and conservation of momentum compares the total momentum vectors before and after a collision, not the vector components with the magnitude of the vector. It makes no sense comparing a vector with a scalar.
 
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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?
(Part of)The problem is in the red sentence. It is not true.

And conservation of a quantity implies a comparison of the values before and after some event or, more general, at two different moments. It has nothing to do with comparing sum of components with magnitude of the vector.
 
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:smile: Thanks for the help!
 

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