Total Displacement Vectors Help

[Helmsy]

Homework Statement

A boat travels West a distance of 200m, then North 400m, and finally 100m South of East at 30 degrees. What is the net displacement.

Homework Equations

none

The Attempt at a Solution

Many attempts none make sense...lol

 

[SteamKing]

If you were to draw a diagram of the different parts of the boat's travels, don't you think that would make this problem easier to solve?

 

[Helmsy]

Yes i have drawn a graph and i just can't figure out how to find the displacement. like i don't know how to even go about finding it

 

[Spinnor]

If you were to draw a diagram of the different parts of the boat's travels, don't you think that would make this problem easier to solve?

Like this? %^)

 

[Helmsy]

ok so Rx= -150 and Ry= 486.6...what do i have to do now to get the net displacement. Thanks for the graphic BTW

 

[issacnewton]

Now try to find R_y

$$\vec{R_y}=\vec{V_{1y}}+\vec{V_{2y}}+\vec{V_{3y}}$$

$$\vec{R_y}=0+400\hat{j}-100\sin{30}\;\hat{j}$$

if the figure drawn by spinnor is correct then , in his equations, there should be
$\cos{30}$ in the equation for $\vec{R_x}$

so the net displacement would be

$$\vec{R}=\vec{R_x}+\vec{R_y}$$

where

$$\vec{R_x}=-200\hat{i}+100\cos{30}\;\hat{i}$$

 

[Helmsy]

ok so if I did my math right the answer should be 336.603. Is that correct?

 

[issacnewton]

I don't know if you are asked to get the answer as a magnitude or a vector. for magnitude I am getting 367.909