Preview Question : AM-10-08-03-04-Q05

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The diagram shows the position and the direction of boats \(A,B\) and \(C\) on a river.

Both boats \(A\) and \(B\) move in the direction of the water current which flow with a velocity of

\(\utilde{w}=\left( 2 \utilde{i}+\dfrac{1}{2} \utilde{j} \right) \text{ ms}^{-1}.\)

The velocity of boat \(A\) is

\(\utilde{a}=\left( \utilde{i}+\utilde{j} \right) \text{ ms}^{-1}.\)

The velocity of boat \(B\) is

\(\utilde{b}=\left( 3 \utilde{i}+2\utilde{j} \right) \text{ ms}^{-1}.\)

Determine how many times the resultant velocity of boat \(B\) compare to the resultant velocity of boat \(A\).

(A)		\(\dfrac{4}{3}\)

(B)		\(\dfrac{5}{3}\)

(C)		\(\dfrac{7}{3}\)

(D)		\(\dfrac{8}{3}\)

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Explanation

Answer: B

Boat A:

Resultant velocity

\(\begin{aligned} &=(\utilde{i} + \utilde{j})+(2 \utilde{i} + \dfrac{1}{2} \utilde{j}) \\\\ &=3 \utilde{i}+\dfrac{3}{2} \utilde{j} \\\\ &=3 \left(\utilde{i}+\dfrac{1}{2}\utilde{j} \right) \text{ ms}^{-1}. \end{aligned}\)

Boat B:

Resultant velocity

\(\begin{aligned} &=(3\utilde{i} + 2\utilde{j})+(2 \utilde{i} + \dfrac{1}{2} \utilde{j}) \\\\ &=5 \utilde{i}+\dfrac{5}{2} \utilde{j} \\\\ &=5 \left(\utilde{i}+\dfrac{1}{2}\utilde{j} \right) \text{ ms}^{-1}. \end{aligned}\)

\(\therefore\) The resultant velocity of boat \(B\) is \(\dfrac{5}{3}\) times the resultant velocity of boat \(A\).

Preview Question : AM-10-08-03-04-Q05

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