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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