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  • A man walking with a speed of 4 km/hr finds the rain drops falling vertically downwards.when the man increases his speed to 8 km/hr he finds that the raindrops are falling making an angle of 30 deg

A man walking with a speed of 4 km/hr finds the rain drops falling vertically downwards.when the man increases his speed to 8 km/hr he finds that the raindrops are falling making an angle of 30 degrees with the vertical. find the speed of the rain drops

Option: 1

4 m/s
 


Option: 2

5 m/s


Option: 3

8 m/s

 


Option: 4

10 m/s


Answers (1)

best_answer

 

Rain - Man Problem -

  • Terminology-

            \overrightarrow{V_{m}}= velocity of man in horizontal direction

             \overrightarrow{V_{r}}= velocity of rain w.r.t ground

            \overrightarrow{V_{r m }}= velocity of rain w.r.t man

 

  • Velocity of rain w.r.t man is given by 

            \overrightarrow{V_{r m }}= \overrightarrow{V_{r }} - \overrightarrow{V_{m }}  

 

As \vec{V_{rm}}= \vec{V_{r}}-\vec{V_{m}}

Initially

{V_{m}}=4\vec{i}

As {V_{rm}}   is vertically downwards and perpendicular to {V_{m}}

\tan \phi = \tan 30= \frac{4}{x}

So from figure x= 4\sqrt{3}

And x=vertical component of {V_{r}}

And from figure Horizontal component of {V_{r}}=4m/s

So {V_{r}}=\sqrt{4^{2}+\left ( 4\sqrt{3} \right )^{2}}= 8m/s

Posted by

Suraj Bhandari

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