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
$(v/a)\,\, sin \,\,\alpha$
✓
$(v/a)\,\, cos \,\,\alpha$
C
$(v/a)\,\, tan \,\,\alpha$
D
$(v/a)\,\,cot \,\,\alpha$

✓

Answer

Correct option: B.

$(v/a)\,\, cos \,\,\alpha$

b
$\nu_{r}$ is subtraction of vectors. Hence,

$\nu_{r}^{2}=x(\operatorname{say})=\nu^{2}+(a t)^{2}-2 v(a t) \cos \alpha$

Now, $\nu_{r}$ will be minimum when $x$ is minimum

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

$\mathrm{t}=\frac{\nu \cos \alpha}{a}$

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