A cat can move at 1ms it wants to get straight across a 2m wide sidewalk moving left at .5 ms what angle should the cat direct itself

moving left? I have never seen a cat do that.

Or is the sidewalk moving left? As in a moving walkway?

If it is a moving walkway, and the cat wants to go straight across, then the cat should head "upstream" at an angle
arc sin (.5/1)=30 degrees

Very odd question. Cats aren't that smart.