Suppose you are travelling in a train. You are sitting inside the train and another train crosses you. Now there could be two scenarios here –

- The second train is moving in the same direction as your train.
- The second train is moving in opposite direction as your train.

How would you- a person sitting inside the train observe the second train? How would the second train look like when it is moving in same direction? How would it look like when moving in opposite direction?

- Second train would appear to you moving faster than usual when moving in opposite direction.
- Second train would appear to you moving slower than usual if it is moving in the same direction.

This phenomenon is used as a mathematical concept called relative speed. So relative speed is the speed at which you saw the other train crossing you in the two scenarios. You considered yourself stationary (as you were sitting inside the first train) and watched the other train crossing you.

Maths of relative speed?

- So when trains are moving in the same directions, sitting inside the train you would see other train crossing slowly – so relative speed here will be = Speed of second train – Speed of first train = V2 – V1

2. So when trains are moving in the opposite direction, sitting inside the train you would see the other crossing fast – So relative speed here will be = Speed of second train + speed of first year = V2 + V1

WHERE TO USE RELATIVE SPEED AND HOW?

So here’s a story. A bunch of robbers enter into a house at 9:00 pm, took hostage of servants and took away cash and important artifacts. When the owner returned to house with his dog, he found servants tied up and house robbed. But the robbers left one handkerchief. The dog was pretty good with sniffing things and catching it. So the owner gave handkerchief to dog and left dog to catch robbers. Dog left the house at 10:00 pm. Now if the robbers are running at a speed of 8kmph and dog is running at a speed of 10 kmph, when will the dog catch those robbers?

__Solutions –__

Okay! So when the dog started running after robbers, it was 10 pm. Means, the robbers would have run for an hour till then.__ __Speed of robber is 8kmph. So in one hour they would have covered 8 kms. So now dog and robbers are separated by 8kms at 10 pm.

Now imagine the time when the dog catches these robbers. The dog covered these 8kms as compared to robbers .Or since the dog and robbers both running in same direction, the dog has to cover this 8km to catch the robbers.

Now the dog is running at a speed of 10kmph. Robbers are running at a speed of 8kmph. Means the relative speed of dog w.r.t robbers = 10-8 =2 kmph. Relative distance of dog and robbers = 8km. Time taken by dog to catch robbers = Time = Relative Distance / Relative Speed = 8/2 =4 Hours.

So the dog will catch robbers at 4 hours after 10pm, means at 2:00 AM.

And hopefully the police will get them at 3?? No we don’t know that !!!!

So this is how we use relative speed , to find out more gyan on races type situations, when will a person cross another one etc. We can also use relative speed to find out time of one object crossing another object when they are travelling in opposite directions.

So in the above figure, the time taken by both the objects to cross each other will be

= D/(V1+V2)