473 A river flows with uniform velocity v relative to its banks. From a dock extending somewhat out into the river, boat A is rowed upstream a distance d at velocity c relative to the water. It then reverses instantaneously and goes down stream to the dock, still being rowed at constant velocity c relative to the water. At the same instant A starts, B also starts across the river, choosing a course (indicated by the dotted path) such that - his ground course is straight across the river, perpendicular to A's path. B also rows a distance d, and both over and back he rows with velocity c with respect to the water. (He also reverses instantaneously). (a) Find the time of each boat to return to the dock, and B show that your results can be written as: A d 2 a 2 d tA and to = (Hint: Be sure to use velocity of boat with respect to ground in both calculations, since d is the ground distance. For B, the velocity of the boat with respect to the water is c along the diagonal path.) (b) If v