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Wind- Origin and its Effects

On a particul...

Question

On a particular day rain was falling vertically with a speed of 30kmhr and wind was blowing from East to west at a speed of 18kmhr. Find the relative velocity of rain w.r.t. Ground.

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Solution

$R a i n f a l l v e l o c i t y v e r t i c a l l y d o w n w a r d s = 30 K m / h . s p e e d o f w i n d E - W = 18 K m / h . t h e r e s u l \tan t s p e e d o f r a i n v = \sqrt{30^{2} + 18^{2}} = \sqrt{900 + 324} = \sqrt{1224} . v = 35 K m / h a p p r o x i m a t e l y i n t h e d i r e c t i o n o f \tan^{- 1} (3 / 5) w i t h t h e v e r t i c a l . \tan θ = \frac{18}{30} = \frac{3}{5} . s o θ = t a n^{- 1} (3 / 5) .$

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