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I am having trouble with the question below and I have read the textbook text many times and I can still not work out how to figure out what the original velocity is relative to the surrounding area, Is there anyone here that could point me in the correct direction please.

A ship is travelling at night in perfectly calm seas at a speed (relative to the surrounding sea) of $40 \text{ km h}^{−1}$ with a bearing of $120^{\circ}$. It is on course to enter harbor in the morning assuming no change in the sea conditions. Unfortunately, during the night, unknown to the crew, a strong current arises, of $10 \text{ km h}^{−1}$ in the direction from south-west to north-east.

Take unit vectors i to point east and j to point north.

Express the original velocity $v$ of the ship relative to the sea and the velocity $c$ of the current in component form, giving the numerical values in $\text{km h}^{−1}$ to one decimal place.

  • 3
    dat title tho${}{}$ – 2017-01-21
  • 0
    Use Carnot Theorem. – 2017-01-21
  • 0
    Looks like R Robinson couldn’t figure this out, either: http://math.stackexchange.com/q/2101996/265466 – 2017-01-21

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You are given the initial velocity in polar form. The $r$ is $40$ and the bearing is measured from North going toward East. Draw a picture with an arrow showing the velocity. You are expected to resolve it into speed North/South and East/West using sines and cosines. Similarly you are supposed to resolve the current into those components. Probably next you are to add the two vectors, but you didn't say that.