Looking at the question above, it is asking to find the speed that the boat will have with respect to a stationary observer on the bank of the canal.
I have set up a vector diagram using the given vectors, and the answer that I am getting is through using the cosine rule.
So what I get is:
$$\sqrt(5.67^2+2.76^2 - 2*cos(60)*2.76*5.67)=$$ resultant speed But, the answer you get is incorrect. Can anyone help?
you can do it like this suppose we sail at an angle $\theta$ w.r.t. ground but we want to sail at an angle 60-degree w.r.t. river
thus $$\tan(60)=\frac{v\sin(\theta)}{v\cos(\theta)+v_c}$$ $$\frac{v\sin(\theta)}{v\cos(\theta)+v_c}=\sqrt3$$ $$\frac{5.67\sin(\theta)}{5.67\cos(\theta)+2.76}=\sqrt3$$ (in picture I have written it $-v_c$ by mistake it should be $+v_c$