Steamboat Captains

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 East-West.
Suppose that your Steamboat travels at 8mph, and the river flows to the East at 6mph.

  1. 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?

  2. 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.
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 vector arithmetic.

If you followed this course, what would the Steamboat's actual speed be (relative to someone watching from outside the river)?

  1. 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.
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 crossing?

Now find the angle you need, to point your boat correctly.

©Copyleft 1995 by Harel Barzilai. "Share and Enjoy." Inspired by Chapter 8 of Why Math? by R.D. Driver.