You are headed for a picnic on Palm Island, which is 5 miles to the
east. The wind, unfortunately, is blowing to the *south*, at 5
miles per hour.

Not to worry! You and your shipmates are master-sailors, and experts at vectors, too!

You point your boat to the east, while angling your sail at a 45° angle to the south-west:

- If we consider the wind as a vector
whose length corresponds to the wind speed in miles per hour, what
vector would represent it?
W = ____________ - If the sail is represented by a
unit-vector emanating from the boat, denoted by S, then
S = ____________ - Now re-draw Figure 1, adding in two
vectors, E (the Effective Wind) and N (the Negligible Wind) into which
W decomposes. Explain (in words) why only E will affect our sail.
- Now identify N as a vector projection:

Can you give a convincing explanation (in words, or orally) to your shipmates as to why this is true?

- Find N
- What two relations (one algebraic,
one geometric) hold between E and N?
- Find E
- This E represents the windforce
which acts (through your sail) on your boat. Find the norm of E, |E|
and interpret its physical significance.
- Due to the keel, no lateral
(sideways) motion is possible for your sailboat; only
forwards/backwards motion.
By now decomposing E into components L (lateral) and F (forwards/backwards), find the force propelling your boat

*eastwards*. How long will it take you to reach Palm Island by this method (assuming the wind remains constant?)

- Same questions, for your trip back from Palm Island.

What happens if you angle your sail at a different angle than 45°?

Can you get better results by doing this? (Your answer will depend, of course, on whether you are in a hurry to get to Palm Island, or want to enjoy a leisurely sailing trip!)

What happens if the wind changes to 5mph North? South-West? At some angle ?