Rain to be falling at an angle 37 degree with vertical to the driver of a car moving with a velocity of 7 metre per second when he increases the velocity of the car to 25 m per second the rain again appers to fall at an angle 37 degree with vertical if the actual velocity of rain related to ground is 4n metre per second then find n.

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Arun · Answer

Angle b/w A & B vectors tan ( α ) = B sin ( θ ) A + B cos ( θ ) where θ = a n g l e b / w A & B v e c t o r s Case 1: Suppose angle b/w A & B is θ , then tan ( 90 0 + 37 0 ) = v r sin ( θ ) 7 + v r cos ( θ ) − c o t ( 37 0 ) = v r sin ( θ ) 7 + v r cos ( θ ) c o t ( 37 0 ) = − v r sin ( θ ) 7 + v r cos ( θ ) ......eq(1) Case 2: tan ( 90 − 37 0 ) = v r sin ( θ ) 25 + v r cos ( θ ) c o t ( 37 0 ) = v r sin ( θ ) 25 + v r cos ( θ ) ...eq(2) from eq...(1) & (2) − v r sin ( θ ) 7 + v r cos ( θ ) = v r sin ( θ ) 25 + v r cos ( θ ) v r cos ( θ ) = − 16 ......eq(3) putting the value of ..eq(3) in eq...(1) we get v r sin ( θ ) = 12 .....eq(4) [ c o t ( 37 0 ) = 4 3 ] from eq.. e q . . ( 3 ) 2 + e q . . ( 4 ) 2 v r 2 = 400 [ sin ( θ 2 ) + cos ( θ 2 ) = 1 ] v r = 20 m / s .....eq(5) putting the value of ..eq(5) into eq..(3) we get cos ( θ ) = − 4 5 θ = 90 0 + 37 0 = 127 0 ...eq(6) So the magnitude of velocity of rain v r = 20 m/s and direction with verticle is at 37 0 angle. Hence velocity = 4n = 20 So n = 5

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