Question Video: Finding the Displacement of a Body Using Vectors Mathematics

If a body moved 10 m due west and then 24 m due south, then total distance covered by the body = ＿ m.

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Video Transcript

If a body moved 10 meters due west and then 24 meters due south, then total distance covered by the body equals blank meters.

One way of answering this question is to simply consider our compass points. We are told that the body initially moves 10 meters due west. It then moves 24 meters due south. As we need to calculate the total distance covered by the body, we simply need to add 10 meters and 24 meters. This is equal to 34 meters. The missing answer is therefore 34.

An alternative method here would be to consider the problem using vectors. We can let the unit vector in the easterly direction equal 𝐢 and the unit vector in the northerly direction equal 𝐣. This means that traveling one meter in the easterly direction equals 𝐢 and moving one meter in the northerly direction equals 𝐣. We can therefore see that the initial movement, 10 meters due west, is equal to negative 10𝐢. Moving 24 meters due south is equal to the vector negative 24𝐣. The displacement vector from start to finish is therefore equal to negative 10𝐢 minus 24𝐣.

To calculate the distance, we would find the sum of the magnitudes of the individual components. The magnitude of negative 10𝐢 is 10, and the magnitude of negative 24𝐣 is 24. This once again gives us an answer of 34 meters.