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Rain is falling at the speed of 25sqrt(3) m/s vertically The wind blows west to east at a speed of 25 m/s. Find the velocity of rain as experienced by a person standing on the ground. I am gettong the value of angle = 30 degrees but it is given 60 degrees in solution.

Rain is falling at the speed of 25sqrt(3) m/s vertically
 The wind blows west to east at a speed of 25 m/s. Find the velocity of rain as experienced by a person standing on the ground.
 
I am gettong the value of angle = 30 degrees but it is given 60 degrees in solution.

Grade:12th pass

1 Answers

Arun
25750 Points
5 years ago
Dear Aabha
 
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 =
       √(625*3+625)  = 50 m / sec

the direction of the resultant velocity vector with the vertical
       = tan ⁻¹ (25/25* root(3)) = 30 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  30 deg. inclination to the vertical  opposite to the direction of wind., towards West.

or,  60  deg. with the horizontal (West)  towards the vertical.
 
Hope it helps
 
Regards
Arun (askIITians forum expert)

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