In the figure, a radar station detects an airplane approaching directly from the east. at first observation, the airplane is at distance d1 = 320 m from the station and at angle θ1 = 31° above the horizon. the airplane is tracked through an angular change δθ = 124° in the vertical east–west plane; its distance is then d2 = 800 m. find the (a) magnitude and (b) direction of the airplane's displacement during this period. give the direction as an angle relative to due west, with a positive angle being above the horizon and a negative angle being below the horizon.

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 = ?