rain is falling vertically with a speed of 35m/s. winds starts blowing after sometimes with a speed of 12m/s in East to west direction .at what angle with the vertical should a boy waiting at a bus stop hold his umbrella yo project himself from rain
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hi,
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 raindrops. 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
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 raindrops. 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
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