Question

A boat is sent across a river with a velocity of $8{kmh}^{-1}$. If the resultant velocity of the boat is $10{kmh}^{-1}$, the river is flowing with a velocity of

• A. $12.8{kmh}^{-1}$
• B. $6{kmh}^{-1}$
• C. $8{kmh}^{-1}$
• D. $10{kmh}^{-1}$

Answer 1

The correct option is B $6{kmh}^{-1}$

The boat is sent across river with velocity $8km/h$ with respect to river perpendicular to it.

Hence $\overrightarrow{v_{br}}=8\hat{j}$

Let the velocity of river $\overrightarrow{v_r}=v\hat{i}$

Hence the resultant velocity of boat $=\overrightarrow{v_{br}}+\overrightarrow{v_r}$ $=\sqrt{v_{br}^2+v_r^2}$

$⟹10=\sqrt{8^2+v^2}$

$⟹v=6km/h$