Question

Two trains each of length $50\,m$, are approaching each other on parallel rails. Their velocities are $10\,m/s$ and $15\,m/s$. They will cross each other in ?

Answer 1

Hint: First start with all the information provided in the question. Here the length of both the trains approaching each other are of equal length so this simplifies the process. Direction of both the trains is towards each other when they are approaching each other hence put the required symbol before their velocities.

Formula used:
The formula of total distance (D) incase two trains are travelling in the same direction is,
$D=2l$
Where, $l$ is the length of the one train.

Complete step by step solution:
Start with the given information from the question:
Length of both the train is $l = 50\,m$
Velocity of both the trains are;
First train’s velocity is $10\,m/s$.
Second train’s velocity is $15\,m/s$.
Now we have to find the distance that is
$D = 2l$
$\Rightarrow D = 2 \times 50 = 100\,m$

Now we have to find the relative velocity as the velocity of the second train is relative to the first train’s velocity. We know that relative velocity,
$v = {v_2} - ( - {v_1})$
$\Rightarrow v = 15 + 10 = 25$
We know that time is distance divided by speed,
$t = \dfrac{D}{v}$
Now put all the values from the above equations, we get;
$t = \dfrac{{100}}{{25}} = 4$
$\therefore t = 4\sec $

Therefore both the trains will cross each other in $4\sec $.

Note: Be careful about the direction of both the trains that is whether they are approaching to each other or are moving apart from each other because we have to put the required symbol as per the direction of the trains before putting the velocities of the train in the respective equations.