Question

Two train 120m and 80m in length are traveling in opposite direction with velocities 42km/h and 30km/h respectively. How much time will they require to completely cross each other?

Answer 1

Answer:

Explanation:

so,in this question,we are expected to solve the case when one train starts crossing the other train,so the rear part of one train has to cross the sum of both the length of trains to completely cross the other train

(here we  consider rear part just becuz it is the last part to cross anythng right)

so the total distance to be covered=120+80=200m

and now we have to use the application of relative velocity.

so,the velocity of first train with respect to second train is equal to velocity of first train-velocity of second train(have to consider the directions also)

so v₁₂=v₁-(-v₂),(here we take -v₂ as the direction is opposite(180°) to the other train.

so we get the effective velocity of one train=42-(-30)=42+30=72km/h=20m/s

(the other train is kept to be stationary applying the constant of relative velocity,see when we took the relative velocity,the other train was assumed to be stationary,i hope u understand this)

so the total distance to be covered is 200m and the effective velocity is 20m/s

so,the time taken to completely cross is 200/20=10sec

(if u draw diagram,u may understand it better)

hope this helps you

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