Two particles start simultaneously from points A and B as shown in the figure. Then what is the minimum distance between them?
A
5m
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B
10m
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C
15m
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D
20m
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Solution
The correct option is B10m Let −−→VAB be the relative velocity of A w.r.t B. −→VA=√10cos45∘^i+√10sin45∘^j ⟹−→VA=√5^i+√5^j −→VB=−√5^j Hence, −−→VAB=−→VA−−→VB=√5^i+2√5^j
Let α be the angle that −−→VAB makes with the line AB. ∴tanα=2√5√5=2 Let dmin be the minimum distance between the particles. From the figure, dmin=5√5sinα=5√5×2√5=10m