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Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity u and the other from rest with uniform acceleration f. Let α be the angle between their directions of motion. The relative velocity of the second particle w.r.t. the first is least after a time t

1. u cos α / f
2. u sin α / f
3. f cos α / u
4. u sin α

Correct answer: u cos α / f

Solution

Relative speed squared = u^2 + (ft)^2 - 2u(ft)cos(alpha). Differentiating with respect to t and setting to zero: 2f^2 t - 2uf cos(alpha)=0, so t = u cos(alpha)/f.

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