Relative speed between two objects

[Husker70]

Homework Statement

Two jets of material from the center of a radio galaxy are ejected in opposite
directions. Both jets move at .750c relative to the galaxy. Determine the speed
of one jet relative to the other.

Homework Equations

u'x = ux-v/1-ux(v)/c^2

The Attempt at a Solution

u' = -.750c - .750c/1-(-.750c)(-.750)/c^2

Is this the right start?
Thanks,
Kevin

 

[borgwal]

Yes, although you might want to take the absolute value in the end to get a relative *speed*, rather than velocity.

I'm assuming here you meant to put some brackets in the right places.

 

[thomate1]

I would like to clarify that the equation you have provided is for the relativistic velocity addition formula, which is used to calculate the velocity of one object relative to another in special relativity. However, in this scenario, we are dealing with the relative speed between two objects, which is different from relative velocity.

To calculate the relative speed between the two jets, we can simply subtract their velocities. Since both jets are moving at 0.750c relative to the galaxy, their relative speed would be 0.750c - (-0.750c) = 1.5c. This means that the two jets are moving away from each other at a relative speed of 1.5 times the speed of light.

It is important to note that this result may seem counterintuitive, as it suggests that the two jets are moving faster than the speed of light relative to each other. However, this is not a violation of special relativity, as the speed of light is the maximum speed that an object can travel in a vacuum. The relative speed between two objects can exceed the speed of light if they are moving in opposite directions, as in this scenario. This is known as the relativistic velocity addition paradox.

In conclusion, the relative speed between the two jets in this scenario is 1.5 times the speed of light. I hope this explanation helps you better understand the concept of relative speed in special relativity.