Question

Two particles A and B are moving with uniform velocity as shown in the figure given below at t = 0.

What is the shortest distance between two particles?

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

${\overrightarrow{v}}_A=10\hat{i},{\overrightarrow{v}}_B=20\hat{j}$

$\therefore v_{BA}=20\hat{j}-10\hat{i}$

$=-10\hat{i}+20\hat{j}$

Initail position of B w.r.t A

For $v_{BA}$,
$\theta =ta{n}^{-1}\frac{20}{10}=ta{n}^{-1}2$

The trajectory of B w.r.t A will be a straight line as the relative velocity remains constant,

As CB=30 and tan$\theta$=2

$\therefore$ EC=60

$\Rightarrow$ OE=20 m (as OC=40 m)

OD will be the shortest distance between A and B.

As tan $\theta$=2, OF=10 m

Tan $\theta$=2, sin $\theta =\frac{2}{\sqrt{5}}$

$\therefore ln\Delta ODF$,

$sin\theta =\frac{2}{\sqrt{5}}=\frac{OD}{OF}=\frac{OD}{10}$

$\Rightarrow OD=\frac{20}{\sqrt{5}}=4\sqrt{5}$