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A man walks at the speed of 4 km/hr. A train coming from behind here at 22 km/hr passes by him in 30 sec. Find the length of the train.

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Hint: Relative speed is defined as the speed of a moving object with respect to another. When two objects are moving in the same direction, relative speed is calculated as their difference. And when the two objects are moving in opposite directions, relative speed is computed by adding the two speeds. Here in the question by just finding the relative speed of the train with respect to the man and applying the distance – time formula we can find the required length of the train.

Complete step by step solution:Speed of the man = 4 km/hr
Speed of the train = 22 km/hr
Since, the train and the man move in the same direction, so we subtract their speed to find the relative speed of the train.
Therefore,
Relative speed of the train = speed of the train – speed of the man
$\begin{array}{l}
{V_R} = 22 - 4\\
 = 18km/hr
\end{array}$
Now, we need to convert km/hr in the m/s unit.
$\begin{array}{l}
{V_R} = 18km/hr\\
 = 5m/s
\end{array}$
Using the distance-time relationship we can easily find the length of the train.
Relative speed of the train = Length of the train time
Therefore, Length of the train
= $\begin{array}{l} 5m/s \times 30s\\
= 150m
\end{array}$
Hence, the length of the train = 150m.


Note: Students should analyze carefully whether they need to add or subtract the speed in order to find the required speed. Unit conversion also becomes crucial in order to get the correct answer.