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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.
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

							Angle b/w A & B vectors                                                     tan(α) = B sin(θ)A + B cos(θ)where θ = angle b/w A & B vectorsCase 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 = 20Son = 5

3 years ago
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