A person walking at 4m/s finds rain drops falling slant wise into his face with a speed of 4 m/s at an angle of $30^{0}$ with the vertical the actual speed of the rain drops is:

4 m/s

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8 m/s

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6 m/s

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5 m/s

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Solution

The correct option is A 4 m/s

The velocity of rain with respect to the man $= 4 m / s$ at an angle 30° with vertical.
Also, it is given that the velocity of the man with respect to ground $= 4 m / s$
The velocity of rain wrt man+velocity of man wrt ground = velocity of rain wrt ground i.e actual velocity of the rain
(by using and applying triangle law of vector addition)
So, velocity of rain wrt ground $= \sqrt{4^{2} + 4^{2} + 2 (4) (4) cos 120}$
$= \sqrt{16 + 16 + 32 (- 0.5)}$
$= \sqrt{32 - 16}$
$= \sqrt{1} 6$
$= 4 m / s$
Therefore the actual velocity of the rain with respect to ground $= 4 m / s$

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A person walking at 4m/s finds rain drops falling slant wise into his face with a speed of 4 m/s at an angle of 300 with the vertical the actual speed of the rain drops is:

A person walking at 4m/s finds rain drops falling slant wise into his face with a speed of 4 m/s at an angle of $30^{0}$ with the vertical the actual speed of the rain drops is: