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

Options

A. `v/a sin alpha`
B. `v/a cos alpha`
C. `v/a tan alpha`
D. `v/a cot alpha`

Answer

B

Explanation

The velocity of first particle , `v_1=v`
The velocity of second particle , `v_2=at`
Relative velocity , `vecv_12 =vecv_1-vecv_2`
or `v_12^2 = v^2 + (at)^2 -2v(at cos alpha)`
For least value of relative velocity , `(dv_12)/(dt)=0`
or `d/(dt)[v^2+a^2 t^2-2 vat cos alpha]=0`
or `0+a^2xx 2t -2vacos alpha = 0` or `t=(v cos alpha)/a`