Question

A river is flowing towards with a velocity of $5m{s}^{-1}$. The boat velocity is $10m{s}^{-1}$. The boat crosses the river by shortest path. Hence,

• A. The direction of boat's velocity is ${30}^{\circ }$ west of north
• B. The direction of boat's velocity is north-west
• C. Resultant velocity is $5\sqrt{3}m{s}^{-1}$
• D. Resultant velocity of boat is $5\sqrt{2}m{s}^{-1}$

Answer 1

Answer: (A), (C)

The correct options are
A The direction of boat's velocity is ${30}^{\circ }$ west of north
C Resultant velocity is $5\sqrt{3}m{s}^{-1}$

For angle $\theta$ in west of north,

$\sin \theta =\frac{5}{10}=0.5,$i.e., $\theta ={30}^o$

$V_r=$resultant velocity

$\sqrt{(10{)}^2-5(5{)}^2}=5\sqrt{3}m{s}^{-1}$

So,options $\left(a\right)$ and $\left(c\right)$ are correct.