Question

Rain is falling vertically with a speed of 35 m/s. Wind start blowing after some time with a speed of 12 m/s in east to west direction. In which direction should a boy waiting at a bus stop hold his umbrella with the vertical? My doubt is why do we take $tan^{-1} (12/35)$ instead of $tan(35/12)$

Answer 1

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The resultant velocity of rain drops will be the vector sum of the rain drop speed (vertical)  and  the horizontal wind speed.

the magnitude of the result velocity of the rain drops =

       √(12²+35²)  = 37 m / sec

the direction of the resultant velocity vector with the vertical

       = tan ⁻¹ (12/35) = 18.92 deg.

The umbrella should be pointed in the direction opposite to the resultant velocity of the rain drops.  So it should be in the direction  18.92 deg. inclination to the vertical  opposite to the direction of wind., towards East.

or,  71.08  deg. with the horizontal (East)  towards the vertical.