vector addition (displacement)

Question

A boat travels 12 km east, then 5 km north. What is the magnitude of net displacement?

RankGuru · Accepted Answer

1. **Vector Components**: East and North directions are perpendicular ($x$ and $y$ axes).
2. **Identify Vectors**: $\vec{d_1} = 12\hat{i}$ and $\vec{d_2} = 5\hat{j}$.
3. **Resultant Vector**: $\vec{R} = 12\hat{i} + 5\hat{j}$.
4. **Magnitude Calculation**: Use the Pythagorean theorem:
   - $|\vec{R}| = \sqrt{x^2 + y^2} = \sqrt{12^2 + 5^2}$
   - $|\vec{R}| = \sqrt{144 + 25} = \sqrt{169} = 13$ km.
5. **Conclusion**: The magnitude of net displacement is **$13$ km**.

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vector addition (displacement)

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