Question

A cruise ship is traveling south going approximately 22 mph when it hits the Gulf Stream flowing east at 4mph.

Show your work.

A) What is the vector component for the cruise ship?

B) What is the vector component for the Gulf Stream?

Answer 1

A) -22j

B) 4i

Explanation:

You want the vector components represented by (a) 22 mph south, and (b) 4 mph east.

Maps and vectors

Maps are generally oriented with North at the top. When compared to an x-y coordinate plane, this means south is in the -y direction, and east is in the +x direction.

Two-dimensional vector spaces are generally defined with unit vector i pointing to the right, and unit vector j pointing up.

Using these conventions, we can define the vector components of the given speeds.

A) 22 mph south

A unit vector in the direction south could be -j. Then the vector component of cruise ship speed in the direction south will be ...

-22j

B) 4 mph east

The unit vector in the direction east will be multiplied by the easterly speed to get the vector component for the Gulf Stream:

+4i

__

Additional comment

A vector is often represented using an over-arrow or a bold or italic font.

`4\vec{i}-22\vec{j}`

In the answer text above, we have used a different font to indicate the unit vectors. The arrows are generally available only in typeset text.

<95141404393>