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Two particles are set in motion at the same instant from a common point along two different straight paths. One particle moves with constant speed v, while the other starts with uniform acceleration a. If the angle between their directions of motion is α, then the time at which the relative velocity becomes minimum is

1. (v)/(a)sinα
2. (v)/(a)cosα
3. (v)/(a)tanα
4. (v)/(a)cotα

Correct answer: (v)/(a)cosα

Solution

The correct option is derived from analyzing the relative velocity between the two particles. The minimum relative velocity occurs when the rate of change of the distance between them is zero, which can be mathematically expressed using the cosine of the angle between their paths, leading to the formula (v)/(a) ext{cos} alpha.

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