question_answer

Rain, pouring down at an angle\[\alpha \]with the vertical has a speed of \[10\text{ m}{{\text{s}}^{-1}}.\] A girl runs against the rain with a speed of \[\text{8 m}{{\text{s}}^{-1}}\] 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) \[\tan \alpha =\cot \beta \]

Correct Answer: B

Solution :

[b] \[\tan \beta =\frac{{{v}_{girl}}+{{v}_{rain}}\sin \alpha }{{{v}_{rain}}\cos \alpha }\] \[\Rightarrow \tan \beta =\frac{8+10\sin \alpha }{10\cos \alpha }\]