# Direction of displacement vector

I got this problem that states:

A boy runs 11.3 blocks North, 5.6 blocks Northeast, and 4.7 blocks West. Determine the length of the displacement vector that goes from the starting point to his final position.

I got the answer to this part. It was 15.25979798 blocks.

Here is the next part:

Determine the direction of the displacement vector. Use counterclockwise as the positive angular direction, between the limits of -180 degrees and +180 degrees measured from the East. Answer in units of degrees.

Now when I drew this out I got a diagram with the first vector going north at 90 degrees, the second vector goes northeast at 45 degrees, and the third vector goes back west at 45 degrees which is back parallel to the x-axis. From the looks of my diagram the head of the final vector stops when it gets to the point where the first vector would have intersected it had it kept going. I entered 90 degrees, but it told me that was wrong. Where did I go wrong? Thanks for the help.

## Answers and Replies

kuruman
Science Advisor
Homework Helper
Gold Member
Do it right. Add the three vectors as vectors and then find the magnitude of the resultant.

PhanthomJay
Science Advisor
Homework Helper
Gold Member
You probably didn't draw it to exact scale. I assume you solved for the magnitude of the displacemnt by using sq rt of sum of squares? The angle is determined using what trigonmetric relationship between the y and x components of the resultant displacement? (Please round off your answers to not more than 1 decimal point).