Question

Two trains A and B, $100m$ and $60m$ long respectively, are moving in opposite directions on parallel tracks. The velocity of the shorter train is $5$ times that of the longer one. If the trains take $2s$ to cross each other, the velocity of the shorter train is

• A. $60.67m/s$
• B. $66.67m/s$
• C. $70.67m/s$
• D. $76.67m/s$

Answer 1

The correct option is B $66.67m/s$

Let the velocity of the longer train be $V$. Then velocity of shorter train $=5V$
Taking the longer train as our observer frame of reference,
velocity of shorter train w.r.t longer train $=5V+V=6V$
Relative distance covered by the shorter train $=100+60=160m$
$\therefore$ Time taken for the trains to cross each other
$t=\frac{160}{6V}=2s$
$\Rightarrow V=\frac{160}{6t}=\frac{160}{6\times 2}=13.33m/s$
Now
$5V=5\times 13.33=66.67m/s$