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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.

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 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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### Course Features

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