Question

one car going to the right with mass 2m with velocity v hits a car going with mass 3m moving at a perpendicular direction with the same speed
what is the final velocity and

Answer 1

The car going in perpendicular to the car moving to the right is not well defined, so it can either go up or down, since both of them are at 90 degrees to the right moving car. In my diagram I have assumed up.

The momentum of the car moving to the right would be mass*velocity=2mv
Similarly for the car moving up, it would be 3mv.

I assume that there would be a collision. Or else the question would be trivial.

Remember that momentum is conserved. In other words, the resultant mess of cars would have 2mv of momentum to the right, and 3mv of momentum up (according to what i assumed).

So by conservation of momentum:
In the right direction, since car up has 0 right-bound velocity:
\[2mv+3m(0)=5mv_{x}\]
and in the up direction, since car right has 0 up-bound velocity:
\[2m(0)+3mv=5mv_{y}\]

To find the magnitude of velocity, simply apply Pythagoras theorem to find the vector sum of velocity:
\[v_{result}=\sqrt{v_{x}^{2}+v_{y}^{2}}=\frac{\sqrt{13}}{5}v\]
For direction you would have to apply some trigonometry.

You can obtain this result by taking the vector sum of 2mv right and 3mv up (see vector sum of velocity). what you find is that the resultant momentum is:
\[\sqrt{13}mv\]

Which is what you get if you take what I got for the resultant velocity and multiply by 5m (total mass after collision.