A certain escalator travels at a rate of 10.6 m/min, and its angle of inclination is 32.5 degrees. What is the vertical component of the velocity? How long will it take a passenger to travel 10.0 m vertically?

v = 10.6

vx = 10.6 cos 32.5
vy = 10.6 sin 32.5

Now that you have vy, the time to travel 10m is just
t = 10/vy