A $2 \ kg$ particle is initially moving in the $x$ direction at $10 \ m/s$ and so has momentum $m*|v| = 20 \ kgm/s$, with components $p_{1x} = -20 kgm/s$, $p_{1y} = p_{1z} = 0$. It hits a second particle initially moving in the $y$ direction with a momentum of $5 kgm/s$. Thus $p_{2x} = p_{2z} = 0$, and $p_{2y} = 5 kgm/s$. The two particles’ total momentum is ?
So apparently total momentum is not just adding $20 \ kgm/s$ and $5 \ kgm/s$. What am I not seeing here?
This is classical mechanics. You can use vector addition. $$ p = p_1 + p_2 = (-20, 0, 0)^\top \text{Ns} + (0, 5, 0)^\top \text{Ns}= (-20, 5, 0)^\top \text{Ns} $$