Question

Two particles start simultaneously from the same point and move along two straight line . 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. $\frac{v}{a}\sin \,\alpha$
• B. $\frac{v}{a}\cos \,\alpha$
• C. $\frac{v}{a}\tan \,\alpha$
• D. $\frac{v}{a}\cot \,\alpha$

Answer 1

Answer: (B)

$\frac{v}{a}\cos \,\alpha$

Answer 2

$\nu_r$ is subtraction of vectors. Hence, $\nu^2_r$ = x(say) = $\nu^2 + (at)^2$ - 2v (at) cos $\alpha$ Now , $\nu_r$ will be minimum when x is minimum Hence $\frac{dx}{dt}$ = 0 or $2a^2 t - 2\nu a$ cos $\alpha$ = 0 t = $\frac{\nu \, \cos \, \alpha}{a}$