Power Practice Test

When riding your bicycle, you have a maximum power output of 500W. As you approach a hill, you shift into first gear, applying a torque of to the gears. Assuming you produce 50% of your maximum power output, what is the angular velocity of the gears, in radians per second?

A crane lifts a crate with a mass of 50kg. The crate is raised at a constant velocity for ten seconds and and moves a vertical distance upwards of 20m. What power is being supplied to the crane during this time?