Question

Rain pouring down at an angle $\alpha$ with the vertical has a speed of $10\text{m/s}$. A girl runs against the rain with the speed of $8\text{m/s}$ and sees that the rain makes an angle $\beta$ with the vertical, then relation between $\alpha$ and $\beta$ is

• A. $\tan \alpha =\frac{8+10\sin \beta }{10\cos \beta }$
• B. $\tan \beta =\frac{8+10\sin \alpha }{10\cos \alpha }$
• C. $\tan \alpha =\tan \beta$
• D. $\tan \alpha =\cot \beta$

Answer 1

The correct option is B $\tan \beta =\frac{8+10\sin \alpha }{10\cos \alpha }$

As per the question, let the condition be as shown in the figure

Given, speed of rain, $V_r=10\text{m/s}$
speed of girl, $V_g=8\text{m/s}$
From the figure we have
$\tan \beta =\frac{V_g+V_r\sin \alpha }{V_r\cos \alpha }=\frac{8+10\sin \alpha }{10\cos \alpha }$