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Question
Two particles A and B, move with constant velocities →v1 and →v2. At the initial moment their position vectors are →r1 and →r2 respectively. The condition for particles A and B for their collision is:
Two particles A and B, move with constant velocities →v1 and →v2. At the initial moment their position vectors are →r1 and →r2 respectively. The condition for particles A and B for their collision is:
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Solution
The correct option is B →r1−→r2∣∣→r1−→r2∣∣=→v2−→v1∣∣→v2−→v1∣∣
For the collision the final position of the both particles should be equal.hence, →r1+→v1t=→r2+→v2tor →r1−→r2=(→v2−→v1)tor →r1−→r2=(→v2−→v1)|→r1−→r2||→v2−→v1|or →r1−→r2|→r1−→r2|=→v2−→v1|→v2−→v1|
For the collision the final position of the both particles should be equal.
hence, →r1+→v1t=→r2+→v2t
or →r1−→r2=(→v2−→v1)t
or →r1−→r2=(→v2−→v1)|→r1−→r2||→v2−→v1|
or →r1−→r2|→r1−→r2|=→v2−→v1|→v2−→v1|
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