Question

# A train of 150 m length is going towards North direction at a speed of $10m{s}^{-1}$. A parrot flies at a speed of $5m{s}^{-1}$ towards South direction parallel to the railway track. The time taken by the parrot to cross the train is equal to

A

$12s$

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B

$8s$

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C

$15s$

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D

$10s$

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E

$5s$

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Solution

## The correct option is D $10s$Step1: Given data and assumptions.Length of the train, $l=150m$Speed of the train, ${v}_{t}=10m{s}^{-1}$Speed of the parrot, ${v}_{b}=5m{s}^{-1}$Step2: Find the time taken by the parrot to cross the train.We haveFrom the figure the relative velocity of the parrot with respect to the train,${v}_{r}={v}_{t}-{v}_{b}$Where ${v}_{r}$ is the relative velocity.${v}_{r}=10-\left(-5\right)$${v}_{r}=15m}{s}$ Now,The time taken by the parrot to cross the train$=\frac{l}{{v}_{r}}$ $=\frac{150}{15}=10s$Hence, option D is correct.

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