Here's a riddle that you may find entertaining and/or pedagogically useful:
Short version:
Do the laws of physics permit a boat to go directly upwind, powered by
wind alone?
This is one of those questions where everybody thinks the answer is
obvious. Interestingly, some people think the answer is obviously yes,
while others think the answer is obviously no.
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Long version: To simplify the terminology, suppose the wind is coming from
due north, and the goal is to travel by boat to a point that is due north
of the starting point.
1) An unsophisticated boat, such as a log raft with a gunny-sack for a
sail, cannot achieve the goal. Indeed it cannot go anywhere north of an
east-west line through the original position.
2) So let's get more sophisticated. Using typical present-day sailboats,
you can achieve the goal indirectly, by sailing to the northeast or
northwest, and then tacking. It's not hard to get a boat that can sail
within 45 degrees of the wind.
3) Can we do even better? Can we make further improvements in the boat
that will allow it to go more directly upwind? (Suppose there is a
minefield, leaving only a straight and narrow opening that goes directly
upwind.) Note that boats lose a lot of energy when they tack, so tacking
at infinitesimally short intervals is not a reasonable solution.
Terms and conditions: Assume the wind is steady and the water is
stationary. The key restriction is that you are not allowed to use any
source of energy other than the wind -- no fuel, no batteries, no galley
slaves, nor any other forms of stored energy.
MAX-PERFORMANCE BOUND: What limits do the laws of physics place on how
close to the wind a boat can go? Please support your claim with a clear
and convincing proof based on the laws of physics. The blue ribbon goes to
the tightest bound, i.e. the course farthest from the wind.
MINIMUM-PERFORMANCE BOUND: Do your best to design a boat that can hold a
course close to the wind. Proof by construction. The blue ribbon goes to
the tightest bound, i.e. the course closest to the wind.