You work for a transport company. Your job is to lift packages from the conveyor belt and slide them up the ramp to your co-worker. The length of the ramp is 6.5 meters, and it is at an angle of 31.0 degrees to the horizontal. The coefficient of friction between the packages and the ramp is 0.330.

a) At what initial speed should you push the package from the bottom end of the ramp so that it stops exactly at the top edge of the ramp?

b) Your colleague is supposed to catch the packages when they arrive at the top of the ramp, but he doesn't catch one of the boxes. What is the speed of the box when it arrives back at you at the bottom of the ramp?