The cosmic rays of highest energy are protons that have kinetic energy on the order of 1013 MeV. (a) From the point of view of the proton, how many kilometers across is the galaxy? (b) How long would it take a proton of this energy to travel across the Milky Way galaxy, having a diameter ~ 105 light-years, as measured in the proton’s frame?

A beam of particles travels by at 2.0*10^8. At this speed you measure them to live 5.00* 10^6  sec, before decaying. What is the particle's life time at rest?

If a proton has a kinetic energy of 1.000 GeV, what is its momentum? (m, = 938.0 MeV/c2 1 Gev = 1000 Mev)

A spacecraft leaves Earth at a constant speed of 0.69c as measured by an observer on Earth. It heads towards a distant star system. The star system is 43.94 lightyears away from Earth, as measured by an observer on Earth. When the spacecraft leaves Earth, the captain of the crew is 24.5 years old. (a) What is the Lorentz γ factor to 3 decimal place precision? (b) What is time taken, in years (to one decimal place precision), to reach the star system as measured by an observer on Earth? (c) What is the distance, in lightyears (to one decimal place precision), the spacecraft travels to reach the star system as measured by the crew of the spacecraft? (d) How old is the captain of the crew when the spacecraft arrives at the star system (use one decimal place precision, and assume the captain can live well beyond normal range of years for a human)? (e) As the spacecraft arrives at the star system, it sends a radio signal back to Earth. Assuming the spacecraft never stops and continues past…

Chapter 37, Problem 045 In a high-energy collision between a cosmic-ray particle and a particle near the top of Earth's atmosphere, 110 km above sea level, a pion is created.The pion has a total energy E of 1.68 x 105 MeV and is traveling vertically downward. In the pion's rest frame, the pion decays 35.0 ns after its creation. At what altitude above sea level, as measured from Earth's reference frame, does the decay occur? The rest energy of a pion is 139.6 MeV. Number Units

One of the many fundamental particles in nature is the muon μ. This particle acts very much like a "heavy electron." It has a mass of 106 MeV/c2, compared to the electron's mass of just 0.511 MeV/c2. (We are using E=mc2 to obtain the mass in units of energy and the speed of light c). Unlike the electron, though, the muon has a finite lifetime, after which it decays into an electron and two very light particles called neutrinos (ν). We'll ignore the neutrinos throughout this problem. If the muon is at rest, the characteristic time that it takes it to decay is about 2.2μs (τμ=2.2×10−6s). Most of the time, though, particles such as muons are not at rest and, if they are moving relativistically, their lifetimes are increased by time dilation. In this problem we will explore some of these relativistic effects. Part A: If a muon is traveling at 70% of the speed of light, how long does it take to decay in the observer's rest frame (i.e., what is the observed lifetime τμ of the muon)? Express…

A deuteron, consisting of a proton and neutron and having mass 3.34 x 10-27 kg, is traveling at 0.950c relative the Earth in a linear accelerator. Calculate the deuteron's rest energy, y-factor, total energy, and kinetic energy. (a) rest energy (Give your answer to at least three significant figures.) (b) y-factor (c) total energy (d) kinetic energy

The proper lifetime of a certain particle is 100.0 ns. How long does it live in the laboratory if it moves at v = 0.860c?

How far from the earth would you be able to travel in a lifetime of 88 years if you were able to travel at a constant speed of 0.67c?

A cosmic ray travels 60 km through the earth’s atmosphere in 400 μs, as measured by experimenters on the ground. How long does the journey take according to the cosmic ray?