Speed of particle Galilean relativity

[j3dwards]

Homework Statement

Two particles are created in a high-energy particle accelerator and move off in opposite directions. The speed of one particle, as measured in the laboratory, is 0.650 c, and the speed of each particle relative to the other is 0.950 c, where c = 3 × 108 m/s is the speed of light in vacuum.

What is the speed of the second particle, as measured in the laboratory? Compare your result to what you would obtain from Galilean relativity.

Homework Equations

u' = u - v

The Attempt at a Solution

So galilean relativity says that the laws of motion are the same in all intertial frames.

So the speed of the second particle is just: 0.950 c - 0.650 c = 0.300 c

correct?

 

[Doc Al]

So the speed of the second particle is just: 0.950 c - 0.350 c = 0.600 c

Earlier you wrote:

The speed of one particle, as measured in the laboratory, is 0.650 c

So there's a typo somewhere.

But that's the right idea for Galilean relativity. What about special relativity?

 

[j3dwards]

Earlier you wrote:

​

So there's a typo somewhere.

But that's the right idea for Galilean relativity. What about special relativity?

Oh yes sorry, so the speed of the second particle is 0.300c.

And for special relativity: u' = u - v/(1-uv/c²) = (0.950c - 0.650c)/(1-(0.95c x 0.650c)/(c²) = 2.35 x 10⁸ = 0.784c

Is this right?

 

[Doc Al]

And for special relativity: u' = u - v/(1-uv/c2) = (0.950c - 0.650c)/(1-(0.95c x 0.650c)/(c2) = 2.35 x 108 = 0.784c

Is this right?

Looks good to me!