Question

A man is walking on a horizontal road with a certain velocity. When it rains vertically downwards, it appears to strike him with double his velocity. The ratio of actual velocity of rain to that of the man is​

Answer 1

Explanation:

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Answer 2

Given info : A man is walking on a horizontal road with a certain velocity. When it rains vertically downwards, it appears to strike him with double his velocity.

To find : the ratio of actual velocity of rain to that of the man is..

solution : let u is the velocity of the man so, $v_m=v\hat i$

a/c to question, it rains vertically downwards and it appears to strike himn with double his velocity.

  so, the velocity of rain with respect to man, $|v_{r,m}|=2v$

and the velocity of the rain,$v_r=-v\hat j$

we know, $v_{r,m}=v_r-v_m$

so, $|v_{r,m}|=\sqrt{v_r^2+v_m^2}$

so, $v_{r,m}^2=v_r^2+v_m^2$

⇒ (2v)² = $v_r^2$ + v²

⇒ $v_r$ = $\sqrt{3}$v

so the ratio of actual velocity of rain to that of the man is $\frac{\sqrt{3}v }{v}$ = $\frac{\sqrt{3} }{1}$