A 15.0 kg k g bucket of water is suspended by a very light rope wrapped around a solid uniform cylinder 0.300 m m in diameter with mass 11.0 kg k g . The cylinder pivots on a frictionless axle through its center. The bucket is released from rest at the top of a well and falls 10.5 m m to the water.

(a) What is the tension in the rope while the bucket is falling?
(b) With what speed does the bucket strike the water?
(c) What is the time of fall?
(d) While the bucket is falling, what is the force exerted on the cylinder by the axle?

At a certain instant after jumping from the airplane a, a skydiver b is in the position shown and has reached a terminal (constant) speed vb = 52 m/s. the airplane has the same constant speed va = 52 m/s, and after a period of level flight is just beginning to follow the circular path shown of radius ρa = 2330 m. (a) determine the velocity and acceleration of the airplane relative to the skydiver. (b) determine the time rate of change of the speed vr of the airplane and the radius of curvature ρr of its path, both as observed by the nonrotating skydiver.