posted by berriengk .
A vessel sails 32 miles S 45 degrees E. How far south has it sailed?
The wording of it confuses me.
Total distance travelled is 32 miles. The south component of the displacement is is 32 cos 45 = 22.63 miles. On a map, that is how much the southern coordinate changes.
There is an eastern displacement of the same amount, 32 sin 45 = 22.63 miles.
The hypotenuse, which is the displacement vector magnitude, is 45 miles
math (correction) -
The hypotenuse, which is the displacement vector magnitude, is 32 miles