A sailboat race is held on a river that runs directly North to South, with a current of 12 knots. A 25 mile race is held going downriver (south). The first heat is held early in the day when there is no wind. The second heat, also going downriver, is held later, when there is a 12 knot tailwind (from the North). In which heat are the fastest times recorded?

(In reply to re(3): solution by Joel)

"I know about tacking and that a boat can move into the wind (in effect).  However, I doubt that it is possible in still water to use a 12 knot wind to move > 12 knots into the wind, just like it is not possible to use the 12 knot wind to move with the wind faster than 12 knots."

The net motion (after taking only the upwind component of the zigzags) need be only say 1 knot. That one knot in consideration of being relative to the surface of the water, would be added to the 12 knots that the water is moving w/r/t the land so the net motion of the boat relative to the land would be 13 knots.  In the second heat it would have no way of being different from 12 knots relative to the land. In the first heat, the air/water entity could have the boat move 1 kt into the (relative) wind, relative to the water, and therefore 13 kt relative to the land.

Consider it as a 12 kt wind over still water. The boat makes progress against it at 1 or 2 kt, say.  Only now consider the land, moving the other way at 12 kt.  The land is moving 13 or 14 kt w/r/t the boat, or vice versa.

Posted by Charlie on 2007-02-14 23:55:57