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A person walking at 4m/s finds rain drops falling slantwise to his face with a speed of 4m/s at an angle of 30 degrees with the vertical. Show that the actual speed of the rain drops is 4m/s
Velocity of rain wrt man= 4m/sat an angle 30º with vertical (given) velocity of man wrt ground = 4m/s from fig. velocity of rain wrt man + velocity of man wrt ground = velocity of rain wrt ground (triangle law of vector addition) so, velocity of rain wrt ground = √(4)2 + (4)2 + 2(4)(4)cos 120 = √ 16+16+32(-0.5) =√32-16 =√16 = 4m/s hence proved!
Velocity of rain wrt man= 4m/sat an angle 30º with vertical (given)
velocity of man wrt ground = 4m/s
from fig.
velocity of rain wrt man + velocity of man wrt ground = velocity of rain wrt ground (triangle law of vector addition)
so, velocity of rain wrt ground = √(4)2 + (4)2 + 2(4)(4)cos 120
= √ 16+16+32(-0.5)
=√32-16
=√16 = 4m/s
hence proved!
Vrm=4 m/sTheta=30°Vmg= 4 m/sAccording to triangle law of vectors,Velocity of man w.r.t ground, Vrg=Vrm + Vmg=Vrg=√4*4 + 4*4 + 2*4*4cos120=√32 - 16=√16=4Hence proved
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