Moving Ship

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Problem:

A ship moves along the equator to the east with velocity $v_0 = 30 \text{km/hour}$. The southeastern wind blows at an angle $\psi= 60^\circ$ to the equator with velocity $v = 15 \text{km/hour}$. Find the wind velocity $v'$ relative to the ship and the angle $\psi$ between the equator and the wind direction in the reference frame fixed to the ship. 

  

Solution:


We have to find $v-v_0$. In other words, we have to find $v+(-v_0)$. At this point, we can simply use vector addition, law of cosines, and law of sines to get that the velocity $$v'=39.7 \text{ at } 19^\circ \text{ from the east}.$$



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