Question

A motor boat is to reach at a point ${30}^o$ upstream (w.r.t. normal) on other side of a river flowing with velocity 5m/s_ The angle ${30}^o$ is measured from a direction perpendicular to river flow. Velocity of motorboat with respect to water is $5\sqrt{3}m/s.$ The driver should steer the boat at an angle

• A. ${120}^o$ with respect to stream direction.
• B. ${30}^o$ with respect to tie perpendicular to the bank.
• C. ${30}^o$ with respect to the line of destination from starting point.
• D. None of these

Answer 1

Answer: (A), (C)

The correct options are
A ${120}^o$ with respect to stream direction.
C ${30}^o$ with respect to the line of destination from starting point.

Kinematics

$V_{mw}$ = relative velocity of boat with respect to water

$\overline{v}m=-\left(5\sqrt{3}\cos \theta \right)i+5\sqrt{3}\cos 30j+5i$

taking $\underset{–}{i}$ direction parallel to river flow and $\underset{–}{j}$ direction ${\underset{–}{l}}^{lar}$ to river flow

${\hat{v}}_m=-7.5i+\frac{5\sqrt{3}}{2}j+5\hat{i}$

${\hat{v}}_m=-2.5i+\frac{5\sqrt{3}}{2}j$

$=ta{n}^{-1}\left[\frac{-5\sqrt{3}}{2\times 2.5}\right]$

$={\tan }^{-1}(-\sqrt{3})$

$={120}^o$ stream direction

velocity of boat ${\overrightarrow{v}}_m=v_{mw}+v_w$