Question

The rowing speed of a man relative to water is $5$ $km/h$ and the speed of water flow is $3$ $km/h$. At what angle to the river flow should he head if he wants to reach a point on the other bank, directly opposite to starting point?

• A. ${127}^0$
• B. ${143}^0$
• C. ${120}^0$
• D. ${150}^0$

Answer 1

The correct option is A ${127}^0$

$v_m=5$ km/h

$v_r=3$ km/h

To reach the directly opposite point the man should move along the line joining the two points in other words due to the resultant velocity his body should flow perpendicular to river flow.

To do this we need to cancel out the speed of water to avoid the drifting. Suppose he moves at angle $90+\theta$ from the direction of flow.

Thus his speed component opposite to that of river is $v_m\sin \theta$

that should cancel $v_r$

i.e., $v_m\sin \theta =v_r$

$\Rightarrow \sin \theta =\frac{3}{5}\Rightarrow \theta ={37}^o$

$\Rightarrow$ angle $=90+37={127}^o$

A is correct.