Kinematics

JEE Main level, single correct, medium

144 of 308

Question 144 of 308

A passenger sitting in a train A moving at 90kmh−190km{h}^{-1} observes another train B moving in the opposite direction for 8s8s. If the velocity of the train B is 54kmh−154km{h}^{-1}, then length of train B is:

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Answer: (B) 320m320m

Let the velocity of A be vA{v}_{A} and the velocity of B be vB{v}_{B}.
The relative velocity is
v⃗BA=v⃗B−v⃗A⇒vBA=54−(−90)=144kmh−1{\vec{v}}_{BA}={\vec{v}}_{B}-{\vec{v}}_{A} \Rightarrow {v}_{BA}=54-(-90)=144km{h}^{-1}
⇒vBA=40ms−1\Rightarrow {v}_{BA}=40m{s}^{-1}
Time=lengthvBATime=\dfrac{length}{{v}_{BA}}
⇒length=40ms−1×8s=320m\Rightarrow length=40m{s}^{-1}\times 8s=320m

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