Question

The particles start simultaneously from the same point and move along two straight lines, one with uniform velocity $\overset{\rightarrow}{u}$ and the other from rest with uniform acceleration $\overset{\rightarrow}{f}$. Let $\alpha$ 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

• A. $\frac{u\sin\alpha}{f}$
• B. $\frac{f\cos\alpha}{u}$
• C. $u\sin\alpha$
• D. $\frac{u\cos\alpha}{f}$

Answer 1

Answer: (D)

$\frac{u\cos\alpha}{f}$

Answer 2

After t, velocity = $f \times t$

$V_{BA} = \overset{\rightarrow}{f}t + ( - \overset{\rightarrow}{u})$

$V_{BA} = \sqrt{f^{2}t^{2} + u^{2} - 2fut\cos\alpha}$

For max. and min., $\frac{d}{dt}(V_{BA}^{2}) = 2f^{2}t - 2fu\cos\alpha = 0$

$t = \frac{u\cos\alpha}{f}$