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. $\left(v/\alpha \right)\sin \alpha$
• B. $\left(v/a\right)\cos \alpha$
• C. $\left(v/a\right)\tan \alpha$
• D. $\left(v/a\right)\cot \alpha$

Answer 1

The correct option is B $\left(v/a\right)\cos \alpha$

$V=a\times t$

$V_{BA}=at+(-u)$

$V_{BA}^2=a^2{t}^2+u^2-2au+cos\alpha$

For maximum and minimum

$\frac{d\left(V_{BA}^2\right)}{dt}=0$

$2a^{2}t-2aucos\alpha$

$t=\frac{ucos\alpha }{a}$

Hence (B) option is correct