Relativistic velocity transformations

[trevorr93]

Homework Statement

An excited nucleus of krypton-80 emits a gamma ray that travels at the speed of light relative to the nucleus. The nucleus itself has a speed of 0.60c relative to the sun. Use a relativistic velocity transformation to determine the speed of the gamma ray relative to the sun if the gamma ray is emitted: a) in the direction of motion of the nucleus and b) opposite to the direction of motion of the nucleus

The Attempt at a Solution

a)

u = u' + v / 1 + vu'/c^2
u = 1 + 0.6 / 1 +(0.6)(1)/c^2
u = 1 c

Does this make sense? Can a particle not move faster then the speed of light?

b) Not sure how to approach this! would a number be negative?

 

[CompuChip]

Looks like you fell for it :-)

A gamma ray is actually just light. That's why it can, and in fact must, travel at the speed of light. What you have shown in a) is one of the postulates of relativity (from which the transformation rule for velocities is derived), namely that light travels at the speed of light for all observers, irrespective of their relative velocity.

Now before you do b), try to think what the answer should be ... then plug in the numbers and see if you are right. If you did get a negative number, how would you explain that?

 

[jayjay713]

oh okay. so b would be equal to 1 as well because of the postulate. thank you for your help!

 

[CompuChip]

Yep*, but you should also be able to get this explicitly from the formula!

*) Actually, almost yep! - I suggest to give it a try anyway.[/size]