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
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