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- 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 0.986c, and an observer who is stationary in a laboratory measures the pion's lifetime to be 2.8 × 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 MO Units UnitsA cylindrical spaceship of length 35.0 m and diameter 8.35 m is traveling in the direction of its cylindrical axis (length). It passes by the Earth at a relative speed of 2.44××1088 m/s. a) What is the length of the ship, as measured by an Earth observer? b) What is the diameter of the ship, as measured by an Earth observer? c) How long does it take the spaceship to travel a distance of 10.0 km according to the ship's pilot? d) How long does it take the spaceship to travel a distance of 10.0 km according to an Earth-based observer?Two spaceships are moving along the line connecting them. One of the spaceships shoots a missile towards the other. The missile leaves the attacking spaceship at 0.955c and approaches the other at 0.755c. What is the relative velocity of the two spaceships? Express it as a ratio to the speed of light. Let the relative velocity of the spaceships be positive if they are approaching each other and negative if they are moving apart from one another.
- a) Find the value of y for the following situation. An astronaut measures the length of his spaceship to be 100 m, while an earthbound observer measures it to be 25 m. b) What is the speed of the spaceship relative to Earth?The starship Enterprise approaches the Klingon home world with speed 0.6c relative to the planet. To announce its arrival, the Enterprise sends a message in a projectile that travels toward the planet with speed 0.4c relative to the Enterprise. At what speed does Klingon at the surface of the planet see the projectile approach? Using relativistic velocity equation.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 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 0.990c, and an observer who is stationary in a laboratory measures the pion's lifetime to be 2.8 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 UnitsA 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 0.992c, and an observer who is stationary in a laboratory measures the pion's lifetime to be 2.7 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
- You have been posted to a remote region of space to monitor traffic. Near the end of a quiet shift, a spacecraft streaks past. Your laser-based measuring device reports the spacecraft’s length to be 85 m. The identification transponder reports it to be the NCXXB-12, a cargo craft of proper length 100 m. In transmitting your report to headquarters, what speed should you give for this spacecraft?Observers in reference frame S see an explosion located at x1=620 m. A second explosion occurs 6.0 micro-s later at x2=1500 m.In reference frame S', which is moving along the +x-axis at speed V, the explosions occur at the same point in space. What is the separation in time delta t' between the two explosions as measured in frame S'? Express your answer in microseconds (micro-s). delta t' = ? micro-sA stationary observer, jack, sees two spaceships, A and B, moving towards him from opposite directions at speeds of Va=0.900c and Vb=0.800c respectively. (Let A be on the left and B on the right, with to-the-right be the positve direction.) a) According to an observer on A, what is Jack's velocity? b) According to an observer on A, what is spaceship B's velocity? c) According to an observer on B, what is Jack's velocity? d) According to an observer on B, what is spaceship A's velocity?