The rate of vibration of a string under constant tension, r cm/s, varies inversely with the length of the string, l cm. When the string is 17 mm long, the rate of vibration is 413 cm/s. Write an equation that describes the rate of vibration of a string in terms of the length of the string.

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 = ?