Question

A man running on a horizontal road at $8kmph$ find that rain is falling vertically. He increases the speed to $12kmph$ and find the drops make an angle ${30}^o$ with the vertical.

• A. The speed of rain is $8\sqrt{3}kmph$
• B. The speed of rain is $8\sqrt{112}kmph$
• C. Speed of rain wrt man is $8kmph$
• D. Speed of rain wrt man is $8\sqrt{3}kmph$

Answer 1

The correct option is C Speed of rain wrt man is $8kmph$

Initial horizontal relative velocity of rain with respect to man is zero.

Because it falling vertically, when man at $u_{xm}=8kmph$.

Final horizontal relative velocity $\left(V_{X\left(RM\right)}\right)$ of rain with respect to man when he is at $V_{xm}=12kmph$

$V_{X\left(RM\right)}=V_m-u_m=12-8=4kmph$

From the figure, $V_{\text{resultant}}$ .Resultant relative velocity of rain with respect to man when he is at $V_{xm}=12kmph$ is

$V_{\text{resultant}}=\frac{V_{X\left(RM\right)}}{\sin {30}^o}=\frac{4}{1/2}=8kmph$

Hence, speed of rain w.r.t man is $8kmph$, when he at velocity $12kmph$ .