Solve Relativity Problem: Proton from Moon to Earth

[dpeagler]

Homework Statement

A cosmic ray proton is moving at a speed of 0.8c as it travels from the moon to the earth. The distance from the moon to the Earth is 3.844*10^5 km (ignore any motions of the Earth and moon). The mass of an electon is 0.511 MeV/c^2 and the proton to electron mass ratio is 1836.15267261(85). Let the proton be in S' and the Earth in frame S.

a. How many seconds does it take for this proton to travel from the moon to the earth?
b. What is the rest energy in MeV of this proton
c. What is the kinetic energy, in MeV, of this proton as seen from earth?
d. What is the total energy, in MeV, of this proton as seen from earth?
e. What is the value of $ sqrt[E^2-(pc)^2] $ in the Earth's frame for this proton

Homework Equations

The Attempt at a Solution

I know how to get b., but am confused about the velocity. Is the velocity relative to Earth or for the proton. I know I can check my answers by solving e. b/c if I am thinking correctly that expresssion in part e. should always be equal to the rest energy mc^2.

If someone could just help me figure out what velocities I'm supposed to be working with I could figure it out. But right now I am just getting confused when I plug the stuff into the momentum equation and kinetic energy equation and so forth.

Thanks for any help.

 

[kuruman]

Relative to the Earth, the proton's speed is 0.8c.
Relative to itself, the proton's speed is zero.