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A particle A moving with a constant velocity of 10m/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 degree with velocity of A .Find the minimum possible magnitude of velocity of B. If they collide after some time.

A particle A moving with a constant velocity of 10m/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 degree with velocity of A .Find the minimum possible magnitude of
    velocity of B. If they collide after some time.


 

Grade:12

2 Answers

askIITianexpert IITDelhi
8 Points
12 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*.866 = 8.66

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

VB = 8.66 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. 

Chaitanya
20 Points
4 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) VB Sinx = 5As Sinx =1VB=5ms

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