Rain appears to be falling at an angle 37°with vertical to the driver of a car moving with a velocity of 7m/s. When he increases the velocity of car to 25 m/s, the rain again appears to fall at an angle 37° with vertical. If the actual velocity of rain related to ground is 4nm/s 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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Rain appears to be falling at an angle 37°with vertical to the driver of a car moving with a velocity of 7m/s. When he increases the velocity of car to 25 m/s, the rain again appears to fall at an angle 37° with vertical. If the actual velocity of rain related to ground is 4nm/s then find n.

Rain appears to be falling at an angle 37°with vertical to the driver of a car moving with a velocity of 7m/s. When he increases the velocity of car to 25 m/s, the rain again appears to fall at an angle 37° with vertical. If the actual velocity of rain related to ground is 4nm/s then find n.

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