A man is walking on a road with a velocity of 3 Km/h when suddenly, it starts raining velocity of rain is 10 Km/h in vertically downward direction, relative velocity of the rain with respect to man is:

The correct option is C $\sqrt{109}$ Km/hr
let the velocity of the rain$V_r=ai+bj$

speed of the rain = $\sqrt{a^2+b^2}$

relative velocity of the rain w.r.t to man is vertical

$V_{rm}=V_r-V_m$ $V_m=3kmph$

$V_m=3i$ $V_r=10kmph$

$V_{rm}=(a-3)i+(b-10)j$

since $V_{rm}$is vertical $a-3=0⟹a=3$ & $b-10=0⟹b=10$

velocity of rain $=\sqrt{3^2+{10}^2}=\sqrt{109}$