A rocketship of proper length o travels at constant velocity v relative to a frame S (see the figure). The nose of the ship (A') passes the point A in S at t=t' = 0, and at this instant a light signal is sent from A' to B'. (a) When, by rocketship time (t), does the signal reach the tail (B) of the ship? (b) At what time t₁, as measured in S, does the signal reach the tail (B') of the ship? (c) At what time t2, as measured in S, does the tail of the ship (B) pass the point A? |A
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- A spaceship leaves the solar system at v = (3/5)c and is headed towards a planet that is 20 c • years away (c is the speed of light). Assume the following: the Sun and the planet are mutually at rest and their clocks have been synchronized such that both read zero when the spaceship leaves. Say that the clock on the ship began at zero. If this is the case, then what should the clock on the ship read when it arrives at the planet?The proper length of one spaceship is three times that of another. The two spaceships are traveling in the same direction and, while both are passing overhead, an Earth observer measures the two spaceships to have the same length. If the slower spaceship has a speed of 0.354c with respect to Earth, determine the speed of the faster spaceship. (Give your answer to at least 3 significant figures.) |cAn object is moving with ordinary speed 0.5c in S reference frame along a direction making an angle (tan 9 = 2) with respect to the positive x - axis. Find the zeroth component of the proper velocity.
- An electron moving at 0.80c relative to the Earth reference frame travels the 100m length of a building (as measured in the Earth reference frame). What is the length of the building according to an observer moving along with the electron?A rod moving relative to an observer is measured to have its length Lmoving contracted to one-half of its length when measured at rest. Find the value of u/c for the rod's rest frame relative to the observer's frame of reference.2.2. A rod of mass m= 1 kg flies with constant velocity past a mark which is stationary in the K frame. In the K frame, it takes the rod At= 20 ns to fly pass the mark, In the K' frame fixed to the rod, the mark moves past the rod in At' = 25 ns. (a) What is the velocity of the rod in the K frame? (b) What is the proper length of the rod? (c) What is the kinetic energy of the rod in the K frame in units of its total energy? (d) What is momentum of the rod in the K frame?
- At relativistic speeds near that of light, the half-life of an unstable particle moving at high speed is longer than when it is at rest. an object is longer when moving than when it is stationary. O light emitted by a moving source moves at the same speed with the same frequency. effects precede causes in some inertial frames. lengths and times only appear different and have no effect on other measurable quantities.A spaceship passes a space-dock at speed 0.5 c. (A) Its length as measured by the space-dock personal is 121 m. What is its length as measured by ship's crew members aboard? (B) The space-ship reaches a planet called Theia in 9.2 days according to the time measured by the space-dock personal. What is this time interval as measured by the ship's captain? (C) Space-ship crew were playing a game on board which took them 65 min to finish one round. How long did the crew memebers take to complete one round of the game as measured by the space-dock personal?A rocket measures 100 m long in its own frame (S') and is travelling at 0.995c relative to a frame S. At the tail of the rocket, a laser sends out a pulse of light which is reflected by a mirror at the nose of the rocket. (a) At what time after emission, measured in S', does the light pulse arrive back at the tail of the rocket? (b) At what time after emission, measured in S, does the light pulse arrive back at the tail of the rocket? (c) What is the spatial distance, measured in S, between the emis- sion of the pulse and its arrival back at the tail of the rocket? (d) At what time after emission, measured in S, does the light pulse hit the mirror? (e) What is the spatial distance, measured in S, between the emis- sion of the pulse and its hitting the mirror? (f) Can you conclude from your answers that the light pulse travelled at a different speed, as seen in S, on its way to the mirror than on the way back? If not, explain your results