A ship sets sail from Rotterdam, The Netherlands intending to head due north at 5.5 m/s relative to the water. However, the local ocean current is 1.5m/s in the direction north of east and changes the ship's intended motion.

Question

a) In what direction would the ship have to travel in order to have a resultant velocity straight north relative to earth, assuming the speed relative to the water remains 5.5 m/s? Specifically the angle west of north, relative to the earth. (i.e. a stationary observer on shore.)
b) what would the ships speed be relative to the earth in m/s?

Can you also show me how the vectors would be pointing to find the straight north resultant velocity? I tried drawing it but the answers were incorrect so I don't know how to do this.
Please help, Thanks!!!

Answer 1

You did not give the current direction except to say it is north of east.
I will say it is y degrees north of east.
In that case the water is moving
Wn = 1.5 sin y is water north speed
We = 1.5 cos y is water east speed

say you head x degrees west of north
Sn = 5.5 cos x = your north speed rel to water
Se = - 5.5 sin x = your east speed rel to water

then relative to solid earth
Vn = 5.5 cos x + 1.5 sin y
Ve = -5.5 sin x+ 1.5 cos y

To go straight north, Ve must be zero
1.5 cos y = -5.5 sin x

I assume you know y but did not tell me. Now find x