Question

the sidewalk moves left at 0.5 m/s. it is 2m long. a cat runs a 1m/s and it wants to run straight across to get to its food. at what angle should the cat direct itself? and how long would the cat take to cross the sidewalk

Answer 1

You did not say if your angle T is measured from across or from upstream. I will do it from across

x - along walk
y across walk
Vc = cat running speed

Vx = Vc sin T - .5 = 0 for result we want
Vy = Vc cos T

so
0 = 1 sin T - .5
sin T = .5
T = 30 degrees

Vy = 1 cos 30 = .866

if cat needs to go 2 m across
2 = .866 t
t = 2.31 seconds