suppose that An boat captain wants to travel due south at 40 knots. If the current is moving northwest at 16 knots, in what direction and magnitude should he work the engine?
here is given picture for simplify
please help
suppose that An boat captain wants to travel due south at 40 knots. If the current is moving northwest at 16 knots, in what direction and magnitude should he work the engine?
here is given picture for simplify
please help
If we represent north as positive on the $y$-axis and east as positive on the $x$-axis, then the vector which gives the velocity of the current is $\vec{v}=16 (\cos 135^\circ,\sin 135^\circ)$. If the ship's absolute velocity must be $(0,-40)$, and the ship's velocity relative to the water is $\vec{w}$, then we have $\vec{v}+\vec{w}=(0,-40)$.
This gives $\vec{w}=(0,-40)-\vec{v}=(-16\cos 135^\circ, -40-16\sin 135^\circ) \approx (11.32,-51,32)$. This has magnitude approximately $r\approx 52.55$ knots and angle $\theta \approx -77.57^\circ$. Here's a visual aid:
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