Mark s): 1
Two trains with speeds 65 m/s and 40 m/s are travelling in the same direction. The train with the higher speed is of shorter length than the other. It can
completely overtake the other train in 20 sec. Now, if they travel in opposite directions and meet at point A, then the slower train takes 4.425 sec extra to pass the point
A after the faster train passes it. What is the difference between the lengths of two trains?
Answers
Answer:
the train 5km only but caluculate
The difference between the lengths of the two trains is 500 m.
Given: Two trains with speeds of 65 m/s and 40 m/s are travelling in the same direction. The faster train can completely overtake the other train in 20 sec.
If they travel in opposite directions and meet at point A, the slower train takes 4.425 sec extra to pass point A after the faster train passes it.
To Find: The difference between the lengths of two trains
Solution:
The question is to be solved using the concept of relative velocity.
- Whenever two bodies ( a and b ) are travelling in the same direction, their relative velocity is given by,
V = Va - Vb [where Va = velocity of a, Vb = velocity of b ]
- Whenever two bodies ( a and b ) are travelling in the opposite direction, their relative velocity is given by,
- V = Va + Vb [where Va = velocity of a, Vb = velocity of b ]
Coming to the numerical, we have;
Va = 65 m/s, Vb = 40 m/s and both trains are travelling in the same direction and completely overtake each other in 20 sec.
∴ the relative velocity V = Va - Vb = 65 - 40 m/s
V = 25 m/s
Now, total relative distance = relative speed × time
= ( 25 × 20 )
= 500 m
Since we have taken the relative velocity when the trains were moving in the same direction, hence, the relative distance is also given by,
S = Sa - Sb [ where Sa = length of train a, Sb = length of train b ]
This relative distance S, in turn, gives us the difference between the lengths of two trains.
So, S = Sa - Sb = 500 m
Hence, the difference between the lengths of the two trains is 500 m.
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