Question

A particle $A$ is moving with a speed $10\text{m/s}$ towards right while particle $B$ is moving at a speed of $10\text{m/s}$ towards right and another particle $C$ is moving at speed of $10\text{m/s}$ towards left. The separation between $A$ and $B$ is $100\text{m}$. Find the time interval between $C$ meeting $B$ and $C$ meeting $A$.

• A. $5\text{s}$
• B. $10\text{s}$
• C. $20\text{s}$
• D. C will never cross A.

Answer 1

The correct option is A $5\text{s}$

The particle $C$ first meets $B$ and then keeps on moving to meet $A$. Hence, the time interval between $C$ meeting $B$ to $C$ meeting $A$ depends on the distance between $A$ and $B$ and relative velocity of $A$ w.r.t $C$.
$t=\frac{\text{Separation between}A\text{and}B}{\text{Relative Velocity}\text{of}A\text{w.r.t}C}$
$t=\frac{100}{10-(-10)}=5\text{sec}$