Question

A boat which has a speed of $5m{s}^{-1}$ in still water crosses the river of width $25\text{m}$ in $10$ seconds. The boat is heading at an angle of $\alpha$ with downstream, where $\alpha$ is equal to

• A. ${150}^{\circ }$
• B. ${120}^{\circ }$
• C. ${90}^{\circ }$
• D. ${60}^{\circ }$

Answer 1

The correct option is A ${150}^{\circ }$

We know that the time taken for the boat to cross the river is given by,

$t=\frac{w}{v\sin \theta }$

Given $w=25\text{m}$ is the width of the river,
time to cross river is $t=10\text{s}$ and
velocity of boat is $v=5m{s}^{-1}$

$\Rightarrow 10=\frac{25}{5\sin \theta }$

$\Rightarrow \sin \theta =\frac{1}{2}$

$\Rightarrow \theta ={30}^{\circ }$
$\therefore \alpha ={180}^{\circ }-\theta ={150}^{\circ }$
$\therefore$ The correct answer is option A