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  4. Rain is falling vertically downwards with a velocity of 4 km / h. A man walks in the rain with a velocity of 3 km / h. The raindrops will fall on the man with a velocity of

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Q. Rain is falling vertically downwards with a velocity of $4\, km / h$. A man walks in the rain with a velocity of $3 \,km / h$. The raindrops will fall on the man with a velocity of

BHUBHU 2008Motion in a Plane

Solution:

Relative velocity of man w.r.t. rain,
image
$\vec{v}_{r m}=\vec{v}_{r}-\vec{v}_{m}$
$=4 \hat{j}-3 \hat{i}$
$=-3 \hat{i}+4 \hat{j}$
or $=5\, km/h|$
$\left|\vec{v}_{r m}\right|=\sqrt{(-3)^{2}+(4)^{2}}$
$=\sqrt{9+16}$
$=\sqrt{25}=5$