Question

In an experiment, two protons are shot directly toward each other, their speed is such that each proton measures a speed of half the speed of light for the other proton.

What does an observer in the laboratory measure for the speeds of these protons?

What is the kinetic energy of each proton as measured by an observer in the lab?

What is the kinetic energy of each proton as measured by the other proton?

Answer 1

let speed of proton be 'x' and mass be 'm'
then speed of then is
x+x=c/2
=>x=c/4
then
M=m(k)
M=m.1/sqrt(1-1/16)
then
KE=mc^2-Mc^2