Two trains are moving in the same direction along parallel tracks....

Two trains are moving in the same direction along parallel tracks. One of them is

200m

long travelling with a velocity of

20ms^{- 1}

. The second one is

800m

long travelling with a velocity of

7. 5ms^{- 1}

. The time taken for the first train to overtake the second is Two trains are moving in the same direction along parallel tracks. One of them is 200m long travelling with a velocity

Two trains are moving in the same direction along parallel tracks. One of them is 200m long travelling with a velocity

Options

A $20s$
B $40s$
C $60s$
D $80s$

Correct answer

D. $80s$

Step-by-step solution

From the figure, the relative displacement is

Two trains are moving in the same direction along parallel tracks. One of them is 200m long travelling with a velocity

{s}_{rel} = \left(800 + 200\right)m = 1000m

{υ}_{rel} = {υ}_{1} - {υ}_{2} = \left(20 - 7.5\right)ms^{- 1}

= 12.5ms^{- 1}

∴ t = \dfrac{srel}{υrel} = \dfrac{1000}{12.5} = 80s

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