Question on relative velocity

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Umm, so as far as I understand velocity is speed in a direction. So if I'm going North at X Km/h and another guy goes south, he'll go at -X Km/h.

So anyways, the formula for relative velocity, for example V(AB) is V(A)-V(B). So let's say two trucks are going at 70 m/s towards each other (they're gonna gonna crash :P).

So the velocity of Truck A relative to Truck B will be 70 m/s - (-70 m/s) = 140 M/S. Now since this is velocity, doesn't this imply that Truck A is going parallel alongside Truck B instead of going the opposite direction.

I'm really sorry if this is a stupid question, this is just a new concept and I don't fully understand it.
 

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  • #2
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No ,,

You can understand it in other way.

Imagine that there is someone on truck A that is moving with 70 km/h . so he will see the other truck 'B' , which is moving with 70 km/h , going with 140 km/h .

Thus , this is the velocity of the truck B relative to A.

v=va-(-vb)

On the other hand , imagine that someone ' let call him X ' is on truck A , that is going parallel alongside truck B and they are moving in the same velocity ,

Now , 'X' will see truck B not moving !! ,,

So the relative velocity is v=va-(-vb)=0.

this is the idea.

Is it understandable now,
:)
 
  • #3
jbriggs444
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So the velocity of Truck A relative to Truck B will be 70 m/s - (-70 m/s) = 140 M/S. Now since this is velocity, doesn't this imply that Truck A is going parallel alongside Truck B instead of going the opposite direction.
As I understand the concern in the OP, this comes down to a question about sign conventions.

The relative velocity of A relative to B is +140 meters/sec if we stay with the convention that North is positive and South is negative. Truck A is moving northward at 140 meters/sec according to truck B.

Edit: This +140 m/s is the calculated "closing velocity" expressed in terms of the ground frame of reference.

But if we adopt the point of view of truck B, it is easy to shift to a convention where front is positive and back is negative. Truck A is moving backward at 140 meters/sec according to truck B.

Edit: This is -140 m/s if expressed in terms of the truck-B-relative frame.

forward and northward in opposite directions. Hence the reversal in sign.
 
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