Originally Posted by bewitched
but the tacking boat must travel a further distance.
at 45 deg tack angle, I'd be an extra 4 km ish
so it's not a matter of making 'any' headway relative to the water, it needs to make enough to cover 14km faster than the other boat does 10 km.
If it's a light sportsboat, it could do it, if it's an old clunker it won't
No, any headway will be enough, because the current is taking both boats towards the finish line at the same VMG. Beyond that, one boat is slowed by the wind, the other is making way into it.
To put it another way, travelling across the stream does not make you any slower towards the finishing line, despite the extra distance. The current is still pulling you in the direction of the finish line
at the same rate.
Think of this exactly analogous
situation, which you get to just by shifting your point of thinking to "relative to the water" from "relative to the land":
Two boats are at rest in the water, with a 5kmh wind on their bows. The "finishing line" is a big piece of string, held at right angles to the wind, moving toward the boats at 5kmh. One boat stays still, pointed into the wind. One boat sails
, tacking into the wind. Which boat will the string hit first?
This is exactly the same scenario.