Question

Rain drops are falling with velocity $(2\hat{i}-4\hat{j})$ m/ s. What should be the velocity of a man so that rain drops hit him with speed 5m/s ?

• A. $-\hat{i}$
• B. $5\hat{i}$
• C. $2\hat{i}$
• D. Both (1) & (2)

Answer 1

The correct option is D Both (1) & (2)

A rain drop is falling with the velocity $\left(2\hat{i}-4\hat{j}\right)m/s$ .

The velocity of the man will be in horizontal direction.

So, let the velocity of the mane be $ai$

So relative velocity of the rain drop w.r.t man will be $\left(2\hat{i}-4\hat{j}\right)m/s$

By the given condition;-

$\begin{array}{c}\left|\left(2-a\right)\hat{i}-4\hat{j}\right|=5\\ \sqrt{{\left(2-a\right)}^2+4^2}=5^2\\ \sqrt{{\left(2-a\right)}^2+4^2}=25\\ {\left(2-a\right)}^2=9\\ \left(2-a\right)=\pm 3\\ So,a=-1or+5\end{array}$

So velocity of the man is $\hat{i}$ or $5\hat{i}$ m/s.