Question:

A delivery truck travels 21 blocks north, 16 blocks east, and 26 blocks south. What is its final displacement from the origin? Assume the blocks are equal length.

Source: Giancoli, Douglas C., Physics: Principles with Applications, 7th Edition, 2014.

Quick Answer:

$17 \textrm{ blocks } [73^\circ \textrm{ E of S}]$

### Transcript for this Giancoli solution

This is Giancoli Answers with Mr. Dychko. This delivery truck initially drives 21 blocks north and then 16 blocks east and 26 blocks south. So its displacement is given by this vector which connects the origin to the destination and it has a*x*-component this way which is equal to the 16 blocks and it has a

*y*-component which is the 26 blocks south minus 21 blocks north for a total of 5 blocks south. So the magnitude of this resultant by using Pythagoras and we have the square root of the

*y*-component of the resultant squared plus the

*x*-component of the resultant squared. So that's square root of 5 squared plus 16 squared and that gives about 17 blocks. And then we'll take this angle in here; this is gonna be the angle to the east of south and that's the inverse tangent of the opposite which is 16 divided by the adjacent which is 5 and that gives about 73 degrees east of south and it's going 17 blocks.

## Comments

Hello why E of S is the same if I said S of E

Hi joseotilio25, is your question "is saying E of S the same as saying S of E"? If so, then nope, those are not the same. Saying $73^\circ$ East of South means $73^\circ$ towards the East, starting from South, whereas S of E means starting at East and measuring $73^\circ$ towards the South.

Hello, I believe Tan should have been reverse (Opposite/Adjacent) so (5/16).

He did do opp/adj. Look at the angle he is looking for in the video.

16/5 is correct.