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Two particles 1 and 2, move with constant velocities v 1 and v 2 .At initial moment their radius vectors are equal to r 1 and r 2 .How must thes particles may be interrelated for the particles to collide?

Two particles 1 and 2, move with constant velocities v1and v2.At initial moment their radius vectors are equal to r1 and r2.How must thes particles may be interrelated for the particles to collide?

Grade:12

1 Answers

Chetan Mandayam Nayakar
312 Points
11 years ago

r1+v1t=r2+v2t, t=(r1-r2)/(v2-v1), t which is a scalar, is a quotient of two vectors. this can be possible only if the two vectors are scalar multiples of each other. so r1-r2=k(v2-v1), where k is a scalar with appropriate dimensions. this implies that

r1-r2 and v2-v1 lie along the same line

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