Question

Two particle start simultaneously from the same point and move along two straight lines, one with uniform velocity $\overrightarrow{u}$ and the other from rest with uniform acceleration $\overrightarrow{f}$. Let $\alpha$ be the angle between their directions of motion. The relative velocity of the second particle with respect to the first 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)

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

After time t,

Velocity = fxt

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

$V_{B{A}^2}=(f^2{t}^2+u^2-2ftu\cos x\alpha [\therefore \alpha$ be the angle between their directions of motion]

for maximum and minimum

$\frac{d}{dt}\left(V_{B{A}^2}\right)=0\Rightarrow 2f^{2}t-2fu\cos \alpha =0$

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