You are the co-captains of an old
Steamboat, the Mississippi Vector. You are currently navigating
it through a half-mile-wide river (not the Mississippi) running
Suppose that your Steamboat travels at 8mph, and the river flows to
the East at 6mph.
If you point your Steamboat North, how long will
it take you to reach the other banks?
Would you arrive where the
sailors are? Why or why not? Draw a triangular diagram depicting the
If you followed this course,
what would the Steamboat's actual speed be (relative to someone
watching from outside the river)?
You are running low on supplies. The two nearest places to
stock up are Drew's Dock, three miles down the river, and Sheila's
Shack, seventeen miles East. If you need supplies A.S.A.P., in which
direction should you point your Steamboat? How long, to the nearest
minute, would each of the two possible trips take?
After loading up on supplies, you continue your travels along
the southern bank of the river, when someone spots what looks like a
stranded party of sailors on the Northern bank, directly across the
river from your boat.
Draw a triangular diagram
depicting the (desired) vector arithmetic.
Without finding the
desired angle "to the left of
straight" for that trek, how long would it take you to make this
Now find the angle you need, to point your boat correctly.
After some consultation, you decide to point your boat at an angle,
so it's headed upstream at exactly the correct angle so it actually
moves directly Northwards.
©Copyleft 1995 by
Harel Barzilai. "Share and Enjoy."
Inspired by Chapter 8 of Why Math? by R.D. Driver.