A particle A is moving with a constant velocity of 10 m/sec. Another particle B is moving with a constant but unknown velocity. At an instant, the line joining A and Bmakes an angle of 30 dgree with velocity of A. Find the minimum possible magnitude of velocity of B. If they collide after some time.

Let V_B makes angle 'x' with the line joining A & B.Then component of both velocities perpendicular to line AB must be equal if they are to meet(collide).

V_B Sinx = V_A Sin(30degree) = 10*1/2 = 5

V_B to be min. Sinx must be max. as their product is a constant.So max(Sinx)=1

V_B = 5 m/s

Here it simply uses the fact that minimum distance of a point from a given line is perpendicular from that point to that line.