As a result of the collisions of cosmic rays with atoms in the upper atmosphere, muon particles are produced kilometers above the Earth's surface. The muon is an unstable particle with a half-life of 1.5 µs. In an experiment, a measurement is made with a muon detector in a balloon 2000 m above the ground, and 650 muons are observed in 1 hour, each of which has a speed of 0.99c in the direction of the Earth. How many of these muons are observed in 1 hour at sea level? (Use No/2^n muons left at the end of the half-life from the No number of muons at the beginning. )

Particle A has a rest energy of 1192 MeV and is moving through the laboratory in the positive x direction with a speed of 0.450c. It decays into particle B (rest energy = 1116 MeV) and a photon; particle A disappears in the decay process. Particle B moves at a speed of 0.400c at an angle of 3.03° with the positive x axis. The photon moves in a direction at an angle with the positive x axis. A 0.45c What are the 0.40c photon Ө 3.03⁰ B in MeVs and your answer in three significant digits. in degrees of the photon? Give

A particle known as a pion lives for a short time before breaking apart into other particles. Suppose a pion is moving at a speed of 0.988c, and an observer who is stationary in a laboratory measures the pion's lifetime to be 3.3 x 10-8 s. (a) What is the lifetime according to a hypothetical person who is riding along with the pion? (b) According to this hypothetical person, how far does the laboratory move before the pion breaks apart? (a) Number (b) Number i Units Units # +

Suppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere produces a muon that has speed v = 0.99c. The muon then travels at constant speed and lives 1.5 μs as measured in the muon's frame of reference. (You can imagine this as the muon's internal clock.)Randomized Variablesv = 0.99 ct = 1.5 μs   Part (a)  How many kilometers does the muon travel according to an Earth-bound observer?  Part (b)  How many kilometers of the Earth pass by as viewed by an observer moving with the muon? Base your calculation on its speed relative to the Earth and its lifetime (proper time).

A positron with a speed of 0.95c collides head-on with an electron going 0.85c in the opposite direction. Find the speed of the positron relative to the electron.