Modern Physics I: Find time from energy

[maherelharake]

Homework Statement

A particle with a rest energy of 2400 MeV has an energy of 15 GeB (15x10^9 eV). Find the time in Earth's frame of reference necessary for this particle to travel from Earth to a star four light-years distant.

Homework Equations

The Attempt at a Solution

I thought about using the rest energy and total energy to find the Kinetic Energy. After that I used the velocity I found and used that to find the time. Is this a good start?

 

[Jack21222]

Homework Statement

A particle with a rest energy of 2400 MeV has an energy of 15 GeB (15x10^9 eV). Find the time in Earth's frame of reference necessary for this particle to travel from Earth to a star four light-years distant.

Homework Equations

The Attempt at a Solution

I thought about using the rest energy and total energy to find the Kinetic Energy. After that I used the velocity I found and used that to find the time. Is this a good start?

That's how I would start it. You might also be able to keep things in terms of c, since the distance is in terms of c. That way you don't need to convert back and forth from m/s.

 

[maherelharake]

Ok thanks. I tried to work it out and this is what I got. I ended up getting a value of 1.26E10 eV for kinetic energy. Using that, I got the ratio v/c to equal .987. I used that to get a time of 4.05 light years for the answer. Any thoughts? Thanks in advance.

 

[maherelharake]

I worked on this problem again today, but couldn't come up with any other way to think about it. If anyone can confirm my above thinking, I will be appreciative.