The Sine River is located between y = sin(x) and y = 1 + sin(x) (x in radians, not degrees).
Your starting point is on the shore, at location (0,0) and your destination is location (5,1).

Your running speed is 1 unit per minute.
Your swimming speed is 1/2 units per minute.

Your plan is to divide the trip into three legs (run, then swim, then run) each leg being a straight line. Assuming there is no current in the river (and no wind), what is the minimum travel time to the destination, and by what pathway?

(In reply to computer solution by Charlie)

If the path had been a constant slope of 1/5 (directly toward the destination) the trip would have taken 5.9759 minutes instead of 5.8853, a difference of .0906 minutes, or 5.436 seconds.

Edited on June 14, 2024, 10:14 pm

Posted by Charlie on 2024-06-14 22:10:02