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Q.

Rain appears to be falling at an angle of 37  with vertical to the driver of a car moving with a velocity of 7m/sec . When he increases the velocity of the car to  25 m/sec , the rain again appears to fall at an angle  37  with vertical. If the actual velocity of rain relative to ground is  4n m/s then find  n.

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answer is 5.

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Detailed Solution

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Let v=  actual velocity of rain and  θ= its angle with vertical: -
Question Image 
In fig. (A),  v sinθ=7+v cosθ tan37=7+34vcosθ
   4v sinθ3v cosθ=28                 (1)
In fig. (B),  25=vsinθ+vcosθtan37=v sinθ+34vcosθ
      4v sinθ+3v cosθ=100            (2)
Solving (1) and (2); we get  v=20 m/s  and  θ=53

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