Kevin S. Huang

2015: Problem 1

Topic: Kinematics
Concepts: Relative velocity, Vectors

Solution:

By the addition of relative velocities, we have

\vec{v}_{\text{boat-ground}}=\vec{v}_{\text{boat-water}}+\vec{v}_{\text{water-ground}}

We are given that these three vectors form a right triangle with hypotenuse $v_{\text{boat-water}}=5\,\mathrm{m/s}$ and $v_{\text{water-ground}}=4\,\mathrm{m/s}$ . Thus,

v_{\text{boat-ground}}=\sqrt{v^2_{\text{boat-water}}-v^2_{\text{water-ground}}}=\sqrt{5^2-4^2}\,\mathrm{m/s}=3\,\mathrm{m/s}

To travel across a distance $d$ , it takes time

t=\frac{d}{v_{\text{boat-ground}}}=\frac{600\,\mathrm{m}}{3\,\mathrm{m/s}}=200\,\mathrm{s}

so the answer is D.

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Kevin S. Huang

2015: Problem 1

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2015: Problem 1

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