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  • A man wearing a hat of extended length 12 cm is running in rain falling vertically downwards with speed 10 m/s. The maximum speed with which man can run, so that rain drops does not fall on his fac

A man wearing a hat of extended length 12 cm is running in rain falling vertically downwards with speed 10 m/s. The maximum speed with which man can run, so that rain drops does not fall on his face (the length of his face below the extended part of the hat is 16 cm) will be :   (please give your answer in m/s)       

        

Option: 1 7.5

Option: 2 13.33

Option: 3 10

Option: 4 0

Answers (1)

best_answer

for

Rain - Man Problem -

tan\Theta = \frac{V_{m}}{V_{r}}\\

\Theta = angle which relative velocity of rain with

            respect to man make with the vertical


 

- wherein

\overrightarrow{V_{r}}= velocity of rain falling vertically

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

 

 

V_{R/G\left ( x \right )}\; \; =0,\; V_{R/G\left ( y \right )}=\; 10 m/s

Let, velocity of man = V

tan\theta =\frac{16}{12}=\frac{4}{3}

then,    V_{R/man}=V (opposite to man)

For the required condition :

tan\theta\; \frac{V\; _{R/M\left ( y \right )}}{V\; _{R/M\left ( x \right )}}=\frac{10}{V}=\frac{4}{3}

\Rightarrow V=\frac{10\times 3}{4}=7.5

Posted by

mansi

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