Question

You are in downtown Chicago (where streets run N-S and E-W). You started from 600 N. Michigan Avenue, and walked 3 blocks toward north, 4 blocks toward west, and 1 block toward north to a train station. Length of one block is 100 [m]. What is the magnitude and direction of your displacement from the start position?

Answer 1

Answer:

Displacement is 565.69 m at 45° west of north

Explanation:

Let north represent positive y axis and east represent positive x axis.

We have journey started from 600 N. Michigan Avenue, and walked 3 blocks toward north, 4 blocks toward west, and 1 block toward north to a train station.

3 blocks toward north = 300 j m

4 blocks toward west = -400 i m

1 blocks toward north = 100 j m

Total displacement = -400 i + 400 j m

Magnitude

     $s=\sqrt{(-400)^2+400^2}=565.69m$

Direction,

     $\theta =tan^{-1}\left ( \frac{400}{-400}\right )=135^0$

     Direction is 45° west of north.

Displacement is 565.69 m at 45° west of north