Question

A train Moving with a speed of 45 km/hr crosses a man walking in the opposite direction at 3.5 km/ hr is 6 seconds. Find the length of the train.​

Answer 1

Given,

• A train moving with speed $45 km/hr.$

• Man moving in opposite direction with speed $3.5 km/hr.$

• Time taken by man to cross the train $6 sec.$

To find,

Length of the train.

Solution,

The problem can be solved using the concept of relative velocity.

The relative velocity is the velocity of an object or observer B in the rest frame of another object or observer A.

To put it in simple words, relative velocity assumes one object to be stationary when observed from the other object.

The formula is,

                                          $v_{ab} = v_{a} - v_{b}$

Where, $v_{ab}$ is velocity of a with respect to b.

Here,

$v_{man} = 3.5km/hr\\ v_{train} = -45km/hr$ ( negative sign because in opposite direction of man)

Now,

                        $v_{man.train} = x_{man} - x_{train} \\v_{man.train} = 3.5km/hr - (-45km/hr)\\v_{man.train} = 48.5km/hr\\v_{man.train} = \frac{485}{36} m/s$

We know that,

                       $speed = \frac{distance}{time}\\ distance = speed*time\\distance = \frac{485}{36}*6 m\\distance = \frac{485}{6}m = 80.833m$

Therefore, the length of train is 80.833m.