A boat can travel at a speed of on still water. A boatman wants to cross a river whilst covering the shortest possible distance. In what direction should he row with respect to the bank if the speed of the water is
Assume that the speed of the water is the same everywhere.
Problem Source : 200 Puzzling Physics Problem
We know that the direction for the shortest possible distance must be perpendicular to the river bank. So for the first sub-problem, the horizontal partial speed must be the same as the speed of the water.
For the second sub-problem, no matter in which direction the boatman rows, he cannot reach the river bank in a perpendicular direction. This can be seen that there is no such fulfill .
Therefore, we solve it in a slightly different way. First, we let the river be still. Relatively, our horizontal partial speed will be and vertical partial speed .
Let the direction of the boat be , so that
Note that the direction of is the angle we move when we row at angle . Our goal is to find the value of such that is maximized.