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

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Detailed Solution

Let $v =$ actual velocity of rain and $θ =$ its angle with vertical: -
Question Image
In fig. (A), $v sin θ = 7 + v cos θ tan 37^{\circ} = 7 + \frac{3}{4} v cos θ$
$\Rightarrow 4 v sin θ - 3 v cos θ = 28$ (1)
In fig. (B), $25 = v \sin θ + v cos θ \tan 37^{\circ} = v sin θ + \frac{3}{4} v cos θ$
$\Rightarrow 4 v sin θ + 3 v cos θ = 100$ (2)
Solving (1) and (2); we get $v = 20 m / s$ and $θ = 53^{\circ}$