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Finding the Velocity Vector in a Vector Word Problem

Elena Rostova • • 2 min read
Finding the Velocity Vector in a Vector Word Problem
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'An ocean liner is supposed to be travelling at 16 km/h on a course of 072°. However, it is drifting off course due to a 3 km/h ocean current which is flowing due west. What is the actual speed and direction of the liner?

I know you need to use vector addition to add the two vectors and then find the resultant vector using the cosine rule, but I don't understand how to find the angle that's needed. I tried 18° and that gave me the velocity, but when I used the sine rule to find the direction, the answer was wrong.

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1 Answer

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Solution idea: You have been given two vectors in what amounts to polar coordinates (a direction and a magnitude). When adding vectors, that's not very convenient. Try converting each of the vectors to rectanglular form (an east component and a north component) (no rules of sine and cosine needed, just right-angled triangles and introductory trigonometry), add them, then convert them back. Drawing a picture will probably help you tremendously.

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Elena Rostova
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Elena Rostova

Elena Rostova holds a Master's degree in Public Health Journalism. She covers groundbreaking medical research, holistic wellness trends, mental health awareness, and nutritional science.