A spaceship has a rest length of 200 meters and it passes by earth at a speed in which only (1/4) x 10-6 s is required for it to pass by a given point as measured by clocks on earth. How fast is it moving?
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A spaceship has a rest length of 200 meters and it passes by earth at a speed in which only (1/4) x 10-6 s is required for it to pass by a given point as measured by clocks on earth. How fast is it moving?

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- 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)A spaceship has a length of 20 meters at rest and accelerates to high speed. A person at rest on the ground observes that the spaceship has 12 meters. How fast (in x 108m/s) is the spaceship?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 spaceship travels from the Earth to a star 13 light years away (as measured in the Earth’s frame). An astronaut on the ship says that the trip takes 16 years. What is the speed of the ship relative to the earth in m/s?A new spaceship is created which can travel so fast that y=20. It travels from Earth to Andromeda. Estimate the distance measured by the astronaut inside the ship.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?A spaceship that has a rest length of 200 m passes by earth at a speed in which only (1/4) x 10-6 s is required for it to pass by a given point as measured by clocks on earth. How fast is it moving and at what length (according to observers on earth)?Two atomic clocks are synchronized. One is placed on a satellite which orbits around the earth at high speeds for a whole year. The other is placed in a lab and remains at rest with respect to the earth. You may assume both clocks can measure time accurately to many significant digits. a)Will the two clocks still be synchronized after one year? b) imagine the speed of light is much lower than its actual value. How would the results of this experiment change if the speed of light was only twice the average speed of the satellite? Explain your reasoning using a calculation.