Question

A boat is moving with the velocity of $4\hat{i}+4\hat{j}$ relative to the stream. The speed of the stream is $-\hat{i}$. What is the displacement of the boat in $10seconds$? (Enter numerical value only)

• A. $40$
• B. $30$
• C. $50$
• D. $20$

Answer 1

Answer: (C)

$50$

$V_{boat/river}=(4\overrightarrow{i}+4\overrightarrow{j})$
$V_{river}=-\hat{i}$
$V_{boat}=V_{boat/river}+V_{river}$
$V_{boat}=(4\overrightarrow{i}+4\overrightarrow{j})+(-\hat{i})=3\hat{i}+4\hat{j}$
$\therefore$ Displacement= velocity $\times$ time= $30\overrightarrow{i}+40\overrightarrow{j}$

or, Magnitude = $\sqrt{{30}^2+{40}^2}=50m$