Two particles start simultaneously from the same point and move along two straight lines, one with uniform…

Two particles start simultaneously from the same point and move along two straight lines, one with uniform velocity $\overrightarrow{\mathrm{u}}$ and the other from rest with uniform acceleration $\overrightarrow{\mathrm{f}}$. 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.
  1. $\frac{u \cos \alpha}{f}$
  2. $\frac{u \sin \alpha}{f}$
  3. $\frac{\mathrm{f} \cos \alpha}{\mathrm{u}}$
  4. u $\sin \alpha$.

Solution

Using ${ }^n C_r+{ }^n C_{r-1}={ }^{n+1} C_r={ }^n C_{r+1}+\underbrace{n} C_{r-1}+{ }^n C_r+{ }^n C_r={ }^n C_{r+1}+{ }^{n+1} C_r+{ }^n C_r$ ${ }^{n+1} C_{r+1}+{ }^{n+1} C_r \Rightarrow{ }^{n+2} C_{r+1}$

Asked in: JEE Main 2003

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