Two particles A and B are located at points 0 , 10 3 and ( 0 , 0 ) in x - y plane. They start moving simultaneously at the time t = 0 s with constant velocities V → A = 5 i ^ m s - 1 and V → B = - 5 3 i ^ m s - 1 , respectively. The time wh

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Two particles A and B are located at points 0 , 10 3 and ( 0 , 0 ) in x - y plane. They start moving simultaneously at the time t = 0 s with constant velocities V → A = 5 i ^ m s - 1 and V → B = - 5 3 i ^ m s - 1 , respectively. The time when they are closest to each other is found to be K / 2 second. Find K . All distances are given in meter.

Quantrex Academy · Accepted Answer

Correct answer: 3

As observed by B motion of A is along AM and BM is the shortest distance between them. Relative displacement of A w.r.t to B is A M = A B cos ⁡ 30 o V → A B = 5 i ^ + 5 3 j ^ Time taken t = S → A B V → A B = A M V A B = 10 3 cos ⁡ 30 o 10 = 1.5 s

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