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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.


3 years ago

Arun
25768 Points
							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 = 20So n = 5.

3 years ago
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• 110 Video Lectures
• Revision Notes
• Test paper with Video Solution
• Mind Map
• Study Planner
• NCERT Solutions
• Discussion Forum
• Previous Year Exam Questions