Two particles start simultaneously from the same point and move a… - Vidyadip

MCQ

Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity $v$ and other with a uniform acceleration $a$. If $\alpha$ is the angle between the lines of motion of two particles, then the least value of relative velocity will be at time given by

A
$\frac{v}{a} \sin \alpha$
✓
$\frac{v}{a} \cos \alpha$
C
$\frac{v}{a} \tan \alpha$
D
$\frac{v}{a} \cot \alpha$

✓

Answer

Correct option: B.

$\frac{v}{a} \cos \alpha$

b
(b)

$v_r$ is subtraction of vector. Hence,

$v_r^2=x($ say $)=v^2+(a t)^2-2 v(a t) \cos \alpha$

Now, $v_r$ will be minimum when $x$ is minimum. Hence,

$\frac{d x}{d t}=0$ or $2 a^2 t-2 v a \cos \alpha=0$

$\therefore \quad t=\frac{v \cos \alpha}{a}$

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