# Relative velocity

1. Sep 28, 2009

### caljuice

1. The problem statement, all variables and given/known dat

So a child is running with the conveyer belt. Relative to the conveyer belt he is running 2.5 m/s.

2. Relevant equations

To find the relative velocity of the child to earth, I'm guesing is:

Velocity of child relative to earth= (v of belt to earth)+(v of child to belt)

If V child-belt = 2.5, that means he is running 2.5 m/s while on the belt right?

So if the child is running against the belt at the same speed, is the equation the same? Is the V child-belt still 2.5 but in the opposite direction?

If i plug in random numbers in the equation for running against the belt, it seems to work still. Say belt is moving 1m/s --> -1.5 m/s= 1 m/s - 2.5 m/s, seems right, he runs -1.5 relative to stationary observers.

But I would assume, since the belt is coming towards the child, the relative velocity of the child to the belt would be greater than 2.5 m/s? and would equal |Velocity of conveyer belt to earth| + |Velocity of child running (not sure what reference frame now)|?

Last edited: Sep 28, 2009
2. Sep 28, 2009

### RoyalCat

Just remember the definition:

$$v_{12}=v_{10}-v_{20}$$

Which, for your case would translate into:

$$v$$child relative to conveyor $$=v$$child relative to earth$$-v$$conveyor relative to earth

3. Oct 1, 2009

### caljuice

The other information was the length of the conveyor and i was suppose to find the acceleration. But I was just confused about the relative velocity.

It seems like as long as I use that equation, it works out. Though I still don't quite understand. If you two people running towards each other should it not be their velocities added for their relative velocity to one another?