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 30o with the vertical.
Initial horizontal relative velocity of rain with respect to man is zero.
Because it falling vertically, when man at uxm=8kmph.
Final horizontal relative velocity (VX(RM)) of rain with respect to man when he is at Vxm=12kmph
From the figure, Vresultant .Resultant relative velocity of rain with respect to man when he is at Vxm=12kmph is
Hence, speed of rain w.r.t man is 8kmph, when he at velocity 12kmph .