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.
Rishabh Gupta , 7 Years ago
Grade 12th pass
1 Answers
Arun
Last Activity: 7 Years ago
Angle b/w A & B vectors tan(α)=Bsin(θ)A+Bcos(θ) where θ=angleb/wA&Bvectors Case 1: Suppose angle b/w A & B is θ, then tan(900+370)=vrsin(θ)7+vrcos(θ) −cot(370)=vrsin(θ)7+vrcos(θ) cot(370)=−vrsin(θ)7+vrcos(θ) ......eq(1) Case 2: tan(90−370)=vrsin(θ)25+vrcos(θ) cot(370)=vrsin(θ)25+vrcos(θ) ...eq(2) from eq...(1) & (2) −vrsin(θ)7+vrcos(θ) = vrsin(θ)25+vrcos(θ) vrcos(θ)=−16 ......eq(3) putting the value of ..eq(3) in eq...(1) we get vrsin(θ)=12 .....eq(4) [cot(370)=43] from eq.. eq..(3)2+eq..(4)2 vr2=400 [sin(θ2)+cos(θ2)=1] vr=20m/s .....eq(5) putting the value of ..eq(5) into eq..(3) we get cos(θ)=−45θ=900+370=1270 ...eq(6) So the magnitude of velocity of rain vr= 20 m/s and direction with verticle is at 370 angle.
Hence velocity = 4n = 20
So
n = 5
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