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3.2 , motion in plane — Physics STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 SciencePhysics3.2 , motion in plane1 Mark
MCQ
In the figure shown, the two projectiles are fired simultaneously. The minimum distance between them during their flight is  ........ $m$
  • A
    $20 $
  • B
    $10\sqrt 3$
  • ✓
    $10$
  • D
    None
✓

Answer

Correct option: C.
$10$
c
Talking origin at a and $x$ axis along $A B$ Velocity of $A$ $w.r.t.$ $B$ $=20 \sqrt{3}(\cos 60 \hat{i}+\sin 60 \hat{j})-20(\cos 150 \hat{i}+\sin 150 \hat{j})$

$=20 \sqrt{3}\left(\frac{1}{2} \hat{i}+\frac{\sqrt{3}}{2} \hat{j}\right)-20\left(-\frac{\sqrt{3}}{2} \hat{i}+\frac{1}{2} \hat{j}\right)=20 \sqrt{3} \hat{i}+20 \hat{j}$

$\tan \theta=\frac{20}{20 \sqrt{3}}=\frac{1}{\sqrt{3}} \Rightarrow \theta=30^{\circ}$

so $\frac{d_{\min }}{20}=\sin \theta=\sin 30^{\circ}=\frac{1}{2} \Rightarrow d_{\min }=10 \mathrm{m}$

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