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Two particles are thrown simultaneously from points A and B with velocities $u_{1} = 2 m s^{- 1}$ and $u_{2} = 14 m s^{- 1}$ respectively, as shown in Fig. Find the minimum separation (in meters) between two particles during their journey

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answer is 9.

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Detailed Solution

Acceleration of B with respect to A is ${\vec{a}}_{B A} = \vec{o}$
${\vec{V}}_{A} = 2 co 45^{0} \hat{i} + 2 \sin 45^{0} \hat{j}$
${\vec{V}}_{B} = 14 co 45^{0} (- \hat{i}) + 14 \sin 45^{0} \hat{j}$
${\vec{V}}_{B A} = 8 \sqrt{2} (- \hat{i}) + 6 \sqrt{2} \hat{j}$
Question Image
$\tan θ = \frac{6}{8} \Rightarrow θ = 37^{0}$
On solving we get $l_{\min} = 9 m$

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