Two-dimensional Motion

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A boat, which has a speed of 10 m/s in still water, is pointed perpendicular to the current of a river flowing at 6 m/s. What is the magnitude of the boat's resultant velocity?

RankGuru · Accepted Answer

1. **Relative Velocity Vector**: The boat's actual velocity $\vec{v}$ is the vector sum of its velocity relative to water $\vec{v}_b$ and the river's velocity $\vec{v}_r$.
2. **Direction**: Since the boat is pointed perpendicular to the flow:
   - $\vec{v} = \vec{v}_b + \vec{v}_r$.
3. **Magnitude (Pythagoras)**:
   - $v = \sqrt{v_b^2 + v_r^2}$.
4. **Calculation**:
   - $v = \sqrt{10^2 + 6^2} = \sqrt{100 + 36} = \sqrt{136}$.
5. **Result**: $v \approx 11.66$ m/s.

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Two-dimensional Motion

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