Question

A 100 m train takes 6 seconds to cross a moving man in the opposite direction at a speed of 5 kmph find the speed of the train

Answer 1

Let the speed of the train with respect to ground be v m/s

The velocity of man in the direction opposite to that of the train is

u = 5 km/h = (5×1000)/(60×60) = 25/18 m/s

So the net velocity of the train with respect to the man running in opposite direction to it is-

vnet = (v+25/18) m/s

It took 6 sec to cover the full length of the train which is 100 m

So, velocity = distance/time

So,

vnet = 100/6
⇒(v+35/18) = 100/6
⇒v = 100/6 − 24/18
⇒v = 376/18 = 188/9


So the velocity of train is 188/9 m/s =

$\frac{188}{9} \times \frac{1}{1000} \times 60 \times 60 = \frac{376}{5} km \: per \: hour$