My first post here: I’m looking for some guidance with a maths problem.
A ship sets sail from England (A) to France (B) covering a distance of 20 miles at an average speed of 5mph. If the ship sails in a straight line from A to B, the voyage should take ~ 4 hours in total.
The ship experiences a sideways current (lateral drift), perpendicular to AB, pushing it off course by 1 mile every hour on average. I’m trying to figure out if the ship’s shortest path will be straight or curved.
I’ve played with some sketches and calculations, showing the ship is best setting out for a destination offset from point B to counter the force of the current.
While one sketch shows a straight line, I’ve also noticed how the navigation problem relates to the Brachistochrone curve. However, I struggled to understand the underlying calculus.
Where can I look to figure out whether the ship’s path is curved or straight, expressed mathematically?
Any pointers appreciated!
Stephen