Question

A man is running up hill with a velocity $(2 \hat{ i }+3 \hat{ j }) m / s$ w.r.t. ground. $He$ feels that the rain drops are falling vertically with velocity $4 m / s$. If he runs down hill with same speed, find $v_{rm}$.

• A. $2 \sqrt{2}\, m / s$
• B. $2 \sqrt{3}\, m / s$
• C. $2 \sqrt{5}\, m / s$
• D. $2 \sqrt{10}\, m / s$

Answer 1

Answer: (C)

$\vec{v}_{ m }=2 \hat{ i }+3 \hat{ j }\, m / s$
$\vec{ v }_{ m }=-4 \hat{ j }\, m / s$
$\vec{ v }_{ r m }=\vec{ v }_{ r }-\vec{ v }_{ m }$
$-4 \hat{ j }=\vec{ v }_{ r }-(2 \hat{ i }+3 \hat{ j })$
$\vec{ v }_{ r }=2 i -\hat{ j }$
Now for downward motion.
$\vec{v}_{ rm }=\vec{ v }_{ r }-\vec{ v }_{ m }=2 \hat{ i }-\hat{ j }+(2 \hat{ i }+3 \hat{ j })=2 \hat{ i }-\hat{ j }+2 \hat{ i }+3 \hat{ j }$
$\vec{ v }_{ rm }=4 \hat{ i }+2 \hat{ j }$
$\Rightarrow \left|\vec{ v }_{ rm }\right|=\sqrt{20}=2 \sqrt{5} m / s$