A man standing on a railway bridge which is 180 m long. He find that a train cross the bridge in 20 seconds but cross him in 8 seconds. Find the length of the train and its speed.
let L be the length of the train.
speed=distance/time=L/8 sec
speed=(180+L)/20
L/8=(180+L)/20
2.5L=180+L
1.5L=180
L=120m
speed=120/8=15 m/s
To find the length of the train, we can use the concept of relative velocity. Let's denote the length of the train as "L" and its speed as "S".
First, let's consider the time it takes for the train to cross the bridge. We know that the total length of the bridge and the train is covered in 20 seconds. So, the relative speed of the train with respect to the man is the distance covered (180 m + L) divided by the time taken (20 seconds). Thus, the relative speed is (180 + L)/20 m/s.
Next, let's consider the time it takes for the train to cross the man. We know that only the length of the train is covered in this case. Therefore, the relative speed of the train with respect to the man is the length of the train (L) divided by the time taken (8 seconds). Thus, the relative speed is L/8 m/s.
Since the relative speed of the train with respect to the man is the same in both cases, we can set up an equation:
(180 + L)/20 = L/8
To simplify this equation, we can cross-multiply:
8(180 + L) = 20L
Simplifying further:
1440 + 8L = 20L
Rearranging the equation:
20L - 8L = 1440
12L = 1440
Dividing both sides by 12:
L = 120
The length of the train is 120 meters.
To find the speed of the train, we can substitute the obtained value of L (120) into one of the previous equations. Let's use:
(180 + L)/20 = S
Substituting L = 120:
(180 + 120)/20 = S
300/20 = S
Simplifying the equation:
S = 15
The speed of the train is 15 m/s.