The positive muon (µ+), an unstable particle, lives on average 2.20 x 10-6 s (measured in its own frame of reference) before decaying. (a) If such a particle is moving, with respect to the laboratory, with a speed of 0.900c, what average lifetime is measured in the laboratory? (b) What average distance, measured in the laboratory, does the particle move before decaying?

An alpha particle has a mass of  6.4E-27kg is propagating at relativistic speeds and has an energy of 6.48GeV (so 6.48E9 eV) What is the speed of the particle, expressed in units of c, c being the speed of light. Keep three significant digits.

A spaceship from another galaxy passes over the solar system directly above a radial line from the sunto the Earth. (We measure the distance between the Earth and the Sun to be 1.496 x 1011 m.) Anobserver standing on the Earth measures that the spaceship is approaching at 0.800c. The Earth-basedobserver also measures that it takes the spaceship 625 seconds to travel from the sun to Earth. Ignorethe relative motion of the Sun and Earth in this problem – their relative speed is only 0.001c, negligiblysmall compared to 0.800c.a) According to a scientist in the spaceship, the Earth-Sun distance is: ______8.9 x 10 ^10__________________b) According to a scientist in the spaceship, the time it takes her to travel the Earth-Sun distance is:_________374 s _______________c) What is the ratio of the kinetic energy to rest energy of the spaceship? KE/ER = _______0.667__________d) As the spaceship passed over the Sun, the alien scientist launched a probe toward Earth, traveling at0.200c relative to…

The lifetime of a free neutron is 886 s. If a neutron moves with a speed of 2.57 ✕ 108 m/s relative to an observer in the lab, what does the observer measure the neutron's lifetime to be (in s)?

The distance to a particular star, as measured in the earth's frame of reference, is 7.11 light- years (1 light-year is the distance that light travels in 1 y). A spaceship leaves the earth and takes 3.35 y to arrive at the star, as measured by passengers on the ship. (a) How long does the trip take, according to observers on earth? (b) What distance for the trip do passengers on the spacecraft measure?

The muon is an unstable particle that spontaneously decays into an electron and two neutrinos. In a reference frame in which the muons are stationary, if the number of muons at t = 0 is N0, the number at time t is given by , where τ is the mean lifetime, equal to 2.2 ms. Suppose the muons move at a speed of 0.95 c and there are 5.0 × 104 muons at t = 0. (a) What is the observed lifetime of the muons? (b) How many muons remain after traveling a distance of 3.0 km?