Two trains are running in opposite direction with the speed 63kmph and 45 kmph respectively then cross each other in 30 seconds.When these trains run in same direction one observer observe that faster train cross slower train in 1 minute. What is length of both train
Answers
Here the velocities of the trains running in opposite directions are taken as 63 km h^(-1) and - 45 km h^(-1).
Velocity of the faster train wrt the slower = 63 - (- 45) = 108 km h^(-1) = 30 m s^(-1).
The distance travelled by the faster train with this velocity when they cross each other is equal to the sum of the length of the trains. Let the length of the faster be L and that of slower be l. So we have,
L + l = 30 t [Here a = 0.]
But t = 30 s here.
Then, L + l = 900 m → (1)
Let the trains run in same direction. Here the velocities are 63 km h^(-1) and 45 km h^(-1).
Now the velocity of the faster wrt the slower = 63 - 45 = 18 km h^(-1) = 5 m s^(-1).
If the observer is from the faster train, then the distance covered by the faster in 1 min = 60 s while traveling in same direction is equal to the length of the slower train. So,
l = 5 × 60 m
l = 300 m → (2)
(1) - (2) implies,
L = 600 m