The average lifetime of a pi meson in its own frame of reference (i.e., the proper lifetime) is 2.6 X 108 s. If the meson moves with a speed of 0.98c, what is (a) its mean lifetime as measured by an observer on Earth, and (b) the average distance it travels before decaying, as measured by an observer on Earth? (c) What distance would it travel if time dilation did not occur?

The star 61 Cygni A is 11.4 light-years from Earth. Imagine a spaceship that travels from Earth to 61 Cygni A at a constant speed of 0.921c. On Earth, we would measure the time it takes for the ship to reach the star to be   11.4 ly 0.921c    = 12.4 years. (a) How much time (in years) would it take the ship to travel from the Earth to the star as measured by a traveler aboard the ship?  years (b) What is the distance to the star (in light years) as measured by a traveler aboard the ship?  ly

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 space traveler takes off from Earth and moves at speed 0.9900c toward the star Vega, which is 26.00 ly distant. How much time will have elapsed by Earth clocks (a) when the traveler reaches Vega and (b) when Earth observers receive word from the traveler that she has arrived? (c) How much older will Earth observers calculate the traveler to be (measured from her frame) when she reaches Vega than she was when she started the trip? (a) Number i (b) Number (c) Number i Units Units Units

HINT (a) What is the momentum (in kg · m/s) of a proton moving at 0.886c? |kg · m/s (b) At what speed (in m/s) will a particle's relativistic momentum equal twice its classical momentum? |m/s

1. You are an observer in a 100-m long spacecraft traveling from the earth to the moon at 0.8c. (a)What is the proper length of the spacecraft? (b) For a proper time interval of 1 sec., the relativistic time interval for the spacecraft measured from the earth reference frame would be: (c)Time dilation does not apply to all time-dependent physical and biological processes. T/F? (c) What is the relativistic length, DL measured from the reference frame of earth? (d) An APOLLO crew left a flat mirror reflector on the surface of the moon (for all you deniers out there, in the 50th anniversary year of APOLLO 11!). If the average surface-to-surface distance from the earth to the moon is 3.83 x 10^8 m, then how long does it take moonlight to reach earth?

Suppose a cosmic ray colliding with a nucleus in the Earth's upper atmosphere produces a muon that has speed v = 0.765c. The muon then travels at constant speed and lives 1.6 μs as measured in the muon's frame of reference. (You can imagine this as the muon's internal clock.)Randomized Variablesv = 0.765 ct = 1.6 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 borg spaceship is in the shape of a cube of side 100.0 m when it is at rest with respect to an observer. What length, width, and height will be the observer witness if the ship flies by at 0.62c going right to left? b) two borq crewmembers are arm wrestling, and it takes 6.0 seconds for the contest to end as measured by a third crewmember. As the ahip flies past the earth at 0.62c, how long will the match last according to an observer on earth?

If ever the human race would need to leave Earth, the Trappist-1 system might make a good destination – the star there has seven temperate terrestrial planets, a few of which are close to Earth’s size and mass. It’s 39.6 light years away, though, so it could take a long time to get there. (a) If the spaceship had a speed of 0.95c, how long would the journey take from the Earth’s reference frame? (b) How long would the journey be for the passengers on the spaceship?

Suppose there is an astronaut who is traveling at a significant fraction of the speed of light.  Part (a) How long, in years, does it take her to travel 4.05 ly at 0.95405c (as measured by the Earth-bound observer)?   Part (b)  How long does it take according to the astronaut in years?