Year 11 Specialist (Unit 1 & 2) Vectors in the Plane

Applications of vectors - relative velocity

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Questions

Question 1

74604

A river is flowing north at 6 km/h. Bertie can swim at 2.5 km/h in still water. He dives in from the east bank and swims to the opposite bank.

i) In which direction does he travel

ii) What is his actual speed?

Answer

i) \(337.4^\circ\)

ii) \(6.5\) km/h

Worked Solution

\begin{align}
&\text{i)}\quad \text{Let}\ \angle NEW=\theta\\
&\begin{aligned}
\therefore \tan \theta&=\frac{6}{2.5} \\
\theta &=67.4^{\circ} \\
\text {True hearing} &=270^{\circ}+67.4^{\circ} \\
&=337.4^{\circ}
\end{aligned}\\
&\begin{aligned}\text{ii)}\quad NE^{2} &=6^{2}+2.5^{2} \\ &=36+6.25 \\
&=42.5 \\
N E &=\sqrt{42.5} \\
&=6.5 \\
\therefore\ &6 . 5 \mathrm{~km} / \mathrm{h} \end{aligned}
\end{align}

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