p03_012.pdf

12. We label the displacement vectors A , B and C (and denote the result

of their vector sum as r ). We

choose east asthe idirection(+ x

direction) and north as the ˆ jdi-

rection (+ y direction). All dis-

tances are understood to be in

kilometers. Therefore,

north

west

east

south

A =3 . 1j

B =

−

2 . 4i

whichmeans

C =

−

5 . 2j

r = A + B + C =

−

2 . 1i

−

2 . 4j

that its magnitude is

= (

−

2 . 1) 2 +(

−

2 . 4) 2

≈

3 . 2km .

and the two possibilities for its angle are

tan − 1 −

2 . 4

=41 ◦ , or 221 ◦ .

−

2 . 1

rectangular “shortcuts” that automaticallyproduce the correct answer for angle

(measured counterclockwise from the + x axis). We may phrase the angle, then, as 221 ◦ counterclockwise

from East (a phrasing that sounds peculiar, at best) or as 41 ◦ south from west or 49 ◦ west from south.

The resultant r is not shown in our sketch; it would be an arrow directed from the “tail” of A to the

“head” of C .

↔

We choose the latter possibility since r is in the third quadrant. It should be noted that many graphical

calculatorshave polar

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