Serway & Jewett — Motion in Two Dimensions: Problem 45

A fisherman sets out upstream on a river. His small boat, powered by an outboard motor, travels at a constant speed \(v\) in still water. The water flows at a lower constant speed \(v_w\). The fisherman has traveled upstream for 2.00 km when his ice chest falls out of the boat. He notices that the chest is missing only after he has gone upstream for another 15.0 min. At that point, he turns around and heads back downstream, all the time traveling at the same speed relative to the water. He catches up with the floating ice chest just as he returns to his starting point. How fast is the river flowing? Solve this problem in two ways. (a) First, use the Earth as a reference frame. With respect to the Earth, the boat travels upstream at speed \(v - v_w\) and downstream at \(v + v_w\). (b) A second much simpler and more elegant solution is obtained by using the water as the reference frame. This approach has important applications in many more complicated problems; examples are calculating the motion of rockets and satellites and analyzing the scattering of subatomic particles from massive targets.