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Question

A policeman is standing on a railway bridge which is $$60$$ meters long. He finds that a train crosses the bridge in $$4\dfrac {1}{2}$$ seconds but himself in $$2$$ seconds. What is the length of the train and its speed


Solution

Let $$x$$ and $$v$$ be the length and speed of train.

Length of platform $$= 60 \; m$$

Time taken by the train to cross the bridge $$= 4 \cfrac{1}{2} = \cfrac{9}{2} s$$
Time taken by the train to cross the policeman $$= 2 s$$
Now,
When the train crosses policeman-

$$t = \cfrac{x}{s}$$

$$\Rightarrow s = \cfrac{x}{2}$$

When the train crosses platform,

$$t = \cfrac{x + 60}{s}$$

$$\cfrac{9}{2} = \cfrac{x + 60}{\tfrac{x}{2}}$$

$$\Rightarrow \cfrac{9}{2} \times \cfrac{x}{2} = x + 60$$

$$9x = 4x + 240$$

$$\Rightarrow 9x - 4x = 240$$

$$\Rightarrow x = \cfrac{240}{5} = 48 \; m$$

Hence the length of train is $$48 \; m$$.

Physics

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