Question

The stream of river is flowing with a speed of 2 km/h. A swimmer can swim at a speed of 4km/h What shouldde me direction of the swimmer with respect to the flow of the river to cross the river straight?(1) 90(2) 120(3) 60(4) 150​

Answer 1

$\color{darkblue}\underline{\underline{\sf Given-}}$

• River speed = 2km/h
• Swimmer speed = 4km/h

$\color{darkblue}\underline{\underline{\sf To \: Find-}}$

• Direction of swimmer with respect to the flow to river to cross the river straight

━━━━━━━━━━━━━━━━━━━━━━━━━━━━

Swimmer to cross the river -

$\implies{\sf v_s\:sin\theta=v_r }$

$\implies{\sf 4\:sin\theta=2}$

$\implies{\sf sin\theta=\dfrac{1}{2}}$

$\color{red}\implies{\sf \theta=30° }$

Direction of swimmer with respect to the flow to river to cross the river straight

$\implies{\sf 90°+30°}$

$\color{red}\implies{\sf 120°}$

$\color{darkblue}\underline{\underline{\sf Answer-}}$

Option (2) 120°

Direction of swimmer with respect to the flow to river to cross the river straight is $\color{red}{\sf 120°}$.