Question

Two particles start simultaneously from the same point and move along two straight lines. One with uniform velocity v and other with a uniform acceleration a. if `alpha ` is the angle between the lines of motion of two particles then the least value of relative velocity will be at time given by
A. `(v)/(a) sin alpha`
B. `(v)/(a) cos alpha`
C. `(v)/(a) tan alpha`
D. `(v)/(a) cot alpha`

Answer 1

Correct Answer - B
At any time velocity of first car is v and that of second car is
`v = v + at = 0 + at`
`v_("rel") = sqrt(v^(2) + (at)^(2) - 2v at cos alpha)`
`v_("rel")` is minimum if `(d)/(dt) (v_(r)^(2)) = 0, t = (v cos alpha)/(a)`