Resultant Velocity of sailing boat

[Purity]

Homework Statement

A boat is sailing on a bearing of 120° and has a speed of 4ms^-1 relative to water. A current has a speed of 2ms^-1 and flows south west.

Find the resultant speed of the boat

2. The attempt at a solution

I've been stuck on this question for an hour now and can't figure out why I'm not getting the correct answer of 3.98ms^-1

If the current is going SW at 225°, (180°+45°), then i have the triangle vbc where b is 2ms^-1 and c is 4ms^-1 and the angle A=105° (225°-120°). (opposite the resultant velocity side v).

I then tried to use the cosine rule which gave me v=4.913...ms which i assumed should've worked.

can someone help me please, I've hit a brick wall again...

 

[Doc Al]

If the current is going SW at 225°, (180°+45°), then i have the triangle vbc where b is 2ms^-1 and c is 4ms^-1 and the angle A=105° (225°-120°). (opposite the resultant velocity side v).

Your angle is wrong. Draw the vector representing the current at 225°. Then from its tip, draw the vector representing the boat's velocity with respect to that current. (You want your triangle to represent the vector sum.) What's the angle between those two side of the triangle?

 

[Purity]

I still don't understand, what I've got drawn is the vertical North axis and line for the boat coming off at 120 degrees and then another line for the current coming off at 225 degrees but they share the same vertex. have i drawn it wrong?

 

[Doc Al]

I still don't understand, what I've got drawn is the vertical North axis and line for the boat coming off at 120 degrees and then another line for the current coming off at 225 degrees but they share the same vertex. have i drawn it wrong?

Looks like you've drawn the vectors with a common origin. Now you have to draw them to represent their sum. So starting with the current, draw its vector as you have done. Then draw the vector representing the boat's speed at 120 degrees starting with its tail at the head of current vector. That's the triangle you want.

(This is often called the 'head to tail' method of graphically adding vectors. The tail of the boat vector starts at the head of the current vector.)

 

[Purity]

Got it, thanks :) I've never heard of a head to tail method before but thank you! the book never mentioned it.