Question

A standing man, observes rain falling with velocity of $20m/s$ at an angle of ${30}^{\circ }$ with the vertical. Now if he further increases his speed, rain again appears to fall at ${30}^{\circ }$ with the vertical. Find his new velocity.

• A. $10\sqrt{3}$ m/s
• B. $20m/s$
• C. $40\sqrt{3}$ m/s
• D. $10m/s$

Answer 1

The correct option is B $20m/s$

${\overrightarrow{v}}_R=-10\hat{i}-10\sqrt{3}\hat{j}$

$\overrightarrow{v{"}_m}=-v_x\hat{i}$

${\overrightarrow{v}}_{RM}=-(10-v_x)\hat{i}-10\sqrt{3}\hat{j}$

Angle with the vertical = ${30}^{\circ }$

$\Rightarrow tan{30}^{\circ }=\frac{10-v+x}{-10\sqrt{3}}\Rightarrow v_x=20m/s$