Question

Rain pouring down at an angle $\alpha$ with the vertical has a speed of $10m{s}^{-1}$. A girl runs against the rain with a speed of $8m{s}^{-1}$ and sees that the rain makes an angle $\beta$ with the vertical. The 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 $\tan \beta =\frac{8+10\sin \alpha }{10\cos \alpha }$

See the diagram,
When the girl moves in direction opposite to rain, due to relative concept, the observed horizontal component of rain increases by 8.
Therefore,
tan $\beta =\frac{(8+10sin\alpha )}{10cos\alpha }$