A rope, under a tension of 114 N and fixed at both ends, oscillates in a second-harmonic standing wave pattern. The displacement of the rope is given by . where at one end of the rope, is in meters, and is in seconds. What are (a) the length of the rope, (b) the speed of the waves on the rope, and (c) the mass of the rope

Two manned satellites approaching one another at a relative speed of 0.550 m/s intend to dock. the first has a mass of 2.50 ✕ 103 kg, and the second a mass of 7.50 ✕ 103 kg. assume that the positive direction is directed from the second satellite towards the first satellite. (a) calculate the final velocity after docking, in the frame of reference in which the first satellite was originally at rest.(b) what is the loss of kinetic energy in this inelastic collision? (c) repeat both parts, in the frame of reference in which the second satellite was originally at rest. final velocity(d) loss of kinetic energy = ?