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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 B makes an angle of 30 dgree with velocity of A. Find the minimum possible magnitude of velocity of B. If they collide after some time.

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 B  makes an angle of 30 dgree with velocity of A. Find the minimum possible magnitude of velocity of B. If they collide after some time.

Grade:11

1 Answers

Khimraj
3007 Points
5 years ago
 

Let VB 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).

VB Sinx = VA Sin(30degree) = 10*1/2 = 5

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

VB = 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. 

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