Velocity of a Boat $A$ boat heads in the direction $\mathrm{N} 72^{\circ} \mathrm{E}$. The speed of the boat relative to the water is $24 \mathrm{mi} / \mathrm{h}$. The water is flowing directly south. It is observed that the true direction of the boat is directly east. (a) Express the velocity of the boat relative to the water as a vector in component form. (b) Find the speed of the water and the true speed of the boat.
Added by Thomas S.
Step 1
Since the boat is heading N 72° E, we can use trigonometry to find these components: Horizontal component (eastward): $24 \cos(72°)$ Vertical component (northward): $24 \sin(72°)$ So the velocity of the boat relative to the water in component form is $\langle 24 Show more…
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A boat heads in the direction $N 72^{\circ} \mathrm{E}$. The speed of the boat relative to the water is $24 \mathrm{mi} / \mathrm{h}$. The water is flowing directly south. It is observed that the true direction of the boat is directly east. (a) Express the velocity of the boat relative to the water as a vector in component form. (b) Find the speed of the water and the true speed of the boat.
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