Calculating Net Displacement Using Vectors

[skp123]

Homework Statement

A bird flies 100m due east from a tree, then 200m northwest (that is 45° north of west). What is the bird’s
net displacement?

Homework Equations

The Attempt at a Solution

I am looking for the formula , which solve this task. We need to use vectors ,but I don't know the formula.

 

[diazona]

Well then, forget about formulas. Can you solve it by drawing a picture? (Maybe on graph paper?) After that, we'll talk about the math.

 

[skp123]

[PLAIN]http://img191.imageshack.us/img191/9901/kokoj.jpg

And now what ? Maybe I needto use this formula S=a*b*cos45

 

[Maybe_Memorie]

[PLAIN]http://img191.imageshack.us/img191/9901/kokoj.jpg

And now what ? Maybe I needto use this formula S=a*b*cos45

It would be easier for you to visualise if you shift the 200 vector to the other side of the 100 vector. Then, break the 200 vector into horizontal and vertical components.
It will be 200Cos45 horizontal and 200Sin45 vertical.
So your net horizontal displacement will be (100 + 200Cos45) and vertical displacement will be 200Sin45.

Now you've got a right angle triangle of displacements, which you can use Pythagoras' Theorem on to solve for the net displacement.

 

[diazona]

[PLAIN]http://img191.imageshack.us/img191/9901/kokoj.jpg

And now what ? Maybe I needto use this formula S=a*b*cos45

For one thing, it would help if you make the drawing to scale. So the 100m line should be half the length of the 200m line, and the angle should really be 45 degrees. (And I would not suggest shifting the vectors as Maybe_Memorie suggested, at least not just yet. The point now is for you to be able to see the path of the bird.)