Movement of the point $A$ on the cylinder

Question

We have a point $A$ on the top of a cylinder with radii $1$.After $2.5$ rolls find the movement of point $A$.(Take $\pi=3$ if needed)

For finding the movement of point $A$ we should use pytagoras to find the movement but I had a disscustion with my teacher about the value of $A'B$ I strongly belive that $A'B=2.5*permiter=2.5*2*\pi=15m$ but our teacher tells that $A'B=2.5*2radii=10m$ I don't know why but I strongly belive my answer.So we decided to ask it here to get an answer .A video will be helpful a lot but I don't know how to make one.Please make for me one or tell me how to make one.Thanks.

Answer 1

Here it is an animation, making the answer trivial:

The distance travelled along the $x$-axis is $5\pi$ and the distance travelled along the $y$-axis is $2$.