![]() Can you solve this problem? You're passively flowing downstream in the middle of a river that has its fastest flow in the middle. Most places along the riverbank are too steep or too vegetated, but suddenly you spot a perfect location for coming ashore a distance y away (measured along the river bank). Note that y can be zero so that you only spot it when you're already drifting past it; or if you're slower still, y can be negative. Now assume your swimming speed is a constant v, while the river's flow is V in the middle and linearly decreasing towards the shore. What angle should you take, as a function of your distance to the shore (x), to reach the desired location using minimum effort (i.e. shortest journey or, equivalently, shortest time)? |
![]() Thanks for reading this far. I'm happy to report that the problem by now has caught others' attention too. That's cool! |