Suppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere produces a muon that has speed v = 0.82c. 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.) 1)how many meters does it travel as observed on the earth? 2)how many meters is this in muon's frame?

A certain type of elementary particle travels at a speed of 2.53 x 108 m/s relative to a lab. The average lifetime in the particle's rest frame is calculated to be 62.6 us. What will be the lifetime of the particle (in us) as measured by someone in the lab? (Use c = 2.9979 × 108 m/s)

The measured mean lifetime of an elementary particle when it is at rest in the lab is measured to be 2.6x10-8 s. If the particle is observed while traveling at a speed v=0.9 c with respect to the lab. What will be the value of the measured mean lifetime while the particle is moving?

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…

An alarm clock is set to sound in 10.0 = h. Att 0, the clock is placed in a spaceship moving with a speed of 0.736 c (relative to Earth). What distance, as determined by an Earth observer, does the spaceship travel before the alarm clock sounds? (Hint: Keep track of your units!) answer in m

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).

The mean lifetime of mesons (pions) is 26 ns. A beam of pions is travelling at 0.93c. As measured in the laboratory: a) What is their mean lifetime? b) How far would they travel before they decay?

A newly constructed spaceship has a length of 100.0 m (as measured in the rest frame). This spaceship departs the Earth, bound for a distant planet located a distance D = 50.0 light-years away from the Earth. It travels at a constant speed of v = 0.900c.   Part A) As measured by Mission Control on Earth, how long does the journey take? Enter the numerical value in units of years. Part B) According to an astronaut on the spaceship, how long does the journey take? Enter the numerical value in units of years. Part C) As measured by Mission Control on Earth, what is the spaceship's apparent length? Enter the numerical value in SI units