Question

suppose an elevator is suspended by a cable that goes around a pulley that has a radius of 1 ft. To the nearest degree, how many degrees of rotation are required for the elevator to ascend or descend 10 ft?

Answer 1

You know the pulley will have to "pull" 10 feet of rope to move the elevator by 10 feet. Therefore, the problem is finding out how much the pulley needs to turn in order for 10 feet of rope to have been pulled up/let down.
You know the circumfernce of the pulley is 2(pi) (remember that the circumference equals 2(pi)(r) ). So you divide 10 by 2(pi) and get ~1.591 which is how many rotations the circle needs to do in order to pull 10 feet of rope.
If it take s~1.591 rotations to move 10 feet of rope, then you can find the number of degrees of rotation by multiplying 1.591 by 360 to get ~572.958

Answer 2

wow thanks!