Question

A man moving with $5m/s$ observes rain falling vertically at the rate of $10m/s$. Find the speed of the rain with respect to ground.

• A. $5\sqrt{5}m/s$
• B. $5m/s$
• C. $3\sqrt{5}m/s$
• D. $8m/s$

Answer 1

The correct option is A $5\sqrt{5}m/s$

At first we have to find out the value of $\theta$
so $tan\theta$=$\frac{1}{2}=0.5$
$\theta$=${\tan }^{-1}0.5=26.56$
so here

velocity of rain w.r.t.man
$V_{rm}=10\times$$cos26.56=8.94$

velocity of man w.r.t groung
$V_{mg}=5\times$$sin26.56=\mathrm{2.2.3}$
so $V_{rg}$=$V_{rm}$+$V_{mg}$=$5\sqrt{5}$