If you kick a rolling ball perpendicularly, what happens?

[Nerkiot]

Hey guys, I've been thinking about inertia/forces for a test I have soon and I've been stumped by a question that the teacher gave us a while ago.

Suppose a football is rolling along the ground and you give it a swift kick in a direction perpendicular to its initial motion. In what direction will it travel if:
a) The ball was initially traveling at a constant speed. (ignore air resistance/friction)
b) The ball was rolling to a stop. (there is air resistance/friction)

Now I think for a) the football will move in the direction of the kick and also veer slightly towards the initial direction due to inertia.
For b) the football will move only in the direction of the kick.

I don't know if I'm right and I can't find a clear explanation on the internet, probably because I'm looking in the wrong places. I know this has something to do with vectors, but I don't see how vectors could explain this, because on one hand you have a velocity vector (the moving ball) and on the other you have a force (the kick).
Can someone please explain what actually happens.

 

[jldibble]

The force acts only while your foot is in contact with the ball, which is a very short amount of time. Afterwards the ball has a velocity vector pointing in both the direction you kicked the ball and the direction the ball was initially moving. Adding these two vectors together will give you a resultant vector which is diagonal to the original movement of the ball.

This would happen in both cases, except the frictional case would make the ball have a slight curve.