Rain is falling vertically with a speed of 35 m/s. Wind starts blowing after sometime 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?
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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.
Hope you got the answer.
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