An object is moving with ordinary speed 0.5c in S reference frame along a direction making an angle (tan 0 =2) with respect to the positive x-axis. Find the components u, and u.,, of the ordinary velocity. And find the components and of the proper velocity.
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- 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.A spaceship departs from a space station and achieves a constant speed of 0.80cwith respect to thes tation, moving directly away from it. The spaceship fires a torpedo forward (in the same direction). The torpedo’s speed with respect to the spaceship is 0.40c. How fast is the torpedo moving with respect to the station?
- Determine an expression for the total travel time of the light pulse, as measured by the following: A) an observer in the S frame (Use the following as necessary: c, d, and v.) B) an observer on the spacecraft (Use the following as necessary: c, d, and v.) What If? If the transmitted light beam has a wavelength λT, determine an expression for the shift in the wavelength of the light beam, as measured by the following C) an observer in the S frame (Use the following as necessary: c, v, and λT.) D) an observer on the spacecraft (Use the following as necessary: c, v, and λT.)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?
- Suppose two angry rhinoceros charge each other. According to a few observers on the ground, the rhinoceros on the left moved to the right at a speed of (1 - ϵ)c while the rhinoceros on the right moved to the left at a speed of (1 - ϵ)c. ϵ is in the range of 0 < ϵ < 1. How fast is the rhinoceros on the right moving in the frame of the rhinoceros on the left? (Show that this speed is less than c, no matter how small ϵ is)A stationary observer O is standing on a platform of length 65 meters on earth. A rocket passes at a velocity of – 0.80c, parallel to the edge of the platform. The observer O notes that at a particular instant the front and back of the rocket simultaneously line up with the ends of the platform. (a) According to O, what is the time necessary for the whole rocket to pass a particular point on the platform? c = 3 × 10% m/s. (b) What is the rest length of the rocket according to an observer O' on the rocket? (c) According to O', what is the length of the platform? 65 m 0.8c O' Figure 2: Problem 4.Calculate the interval ∆s2 between two events with coordinates ( x1 = 50 m, y1 = 0, z1 = 0,t1 = 1 µs) and (x2 = 120 m, y2 = 0, z2 = 0, t2 = 1.2 µs) in an inertial frame S. b) Now transform the coordinates of the events into the S'frame, which is travelling at 0.6calong the x-axis in a positive direction with respect to the frame S. Hence verify that thespacetime interval is invariant.