1. ## vector word problem

Hi guys,

the question i am workinflg on is:

A ship is required to travel south at a speed of 20km/h. There is a current of 6km/h from the southwest

I am trying to work out the direction the ship must head to compensate for the current and the speed the ship must travel in order to achieve its speed of 20km/h.

I have started by looking at the vector current and calculating its i and j components which i found to be each 6/sqrt2.

I am a bit stuck now and would really appreciate some help, thanks!

2. ## Re: vector word problem

Let $\vec{i}$ be the unit "east" vector and let $\vec{j}$ be the unit "north" vector. The ship's velocity (or any vector) can be written $a\vec{i}+ b\vec{j}$. You are given that the desired velocity is $-20\vec{j}$ and you have correctly calculated that the current's velocity is $3\sqrt{2}\vec{i}+ 3\sqrt{2}\vec{j}$. Those must add to the desired velocity. Solve $a\vec{i}+ b\vec{j}+ 3\sqrt{2}\vec{i}+ 3\sqrt{2}\vec{j}= (a+ 3\sqrt{2})\vec{i}+ (b+ 3\sqrt{2})\vec{j}= 0\vec{i}- 20\vec{j}$.

3. ## Re: vector word problem

Hi sorry, where does 3sqrt2 come from ( i got 6/ sqrt2 for i and j from the 45 degree triangle formed by the current vector)

4. ## Re: vector word problem

Have you never heard of "rationalizing the denominator"?