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Grade: 12th pass

                        

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.

3 years ago

Answers : (1)

Arun
24742 Points
							
Angle b/w A & B vectors
                                                     tan(α) = B sin(θ)A + B cos(θ)
where θ = angle b/w A & B vectors
Case 1: Suppose angle b/w A & B is θ, then
                                                    tan(900+370) = vr sin(θ)7 + vr cos(θ)
                                                          cot(370) = vr sin(θ)7 + vr cos(θ)
                                                          cot(370) = vr sin(θ)7 + vr cos(θ)          ......eq(1)
Case 2:
                                                           tan(90 370) = vr sin(θ)25 + vr cos(θ)
  
                                                          cot(370) = vr sin(θ)25 + vr cos(θ)                      ...eq(2)
from eq...(1) & (2)
  
                                                        vr sin(θ)7 + vr cos(θ) = vr sin(θ)25 + vr cos(θ)
  
                                                                 vr cos(θ) = 16                                ......eq(3)
putting the value of ..eq(3) in eq...(1) we get
  
                                                                vr sin(θ) = 12               .....eq(4)      [cot(370) = 43]
from eq.. eq..(3)2 + eq..(4)2
    
                                                                vr 2 = 400                                                              [sin(θ2) + cos(θ2) = 1]
    
                                                                vr = 20 m/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
3 years ago
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