A plank, fixed to a sled at rest in a stationary frame S , is of length Lo and makes an angle of 44° with the x-axis. Later, the sled zooms through frame S at a constant velocity v parallel to the x-axis and the angle appears to be 60° relative to the x-axis in frame S . What is the speed of the sled in terms of c, the speed of light in vacuum?
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A plank, fixed to a sled at rest in a stationary frame S , is of length Lo and makes an angle of 44°
with the x-axis. Later, the sled zooms through frame S at a constant velocity v parallel to the x-axis and
the angle appears to be 60° relative to the x-axis in frame S . What is the speed of the sled in terms of c,
the speed of light in vacuum?
Given:
The original length of the rod is L0
In the rest frame, the rod oriented in the angle is
When the frame moves with constant velocity, the rod is oriented at an angle that is
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- An experimenter has studied the decay of a K° particle in which it emits a 7° at 0.8c. One such K° particle passes the experimenter at 0.5c and decays, emitting a 7° in the original direction of motion. In the experimenter's frame, the speed of the T° is measured to be O 1.3c. O between c and 1.3c. between .5c and .8c. O between .8c and c..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?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?
- Earth and a star are 20 light years (ly) apart, measured in a frame at rest with respect to Earth and star. Twin A boards a spaceship, travels at 0.80c to the star, and then returns immediately to Earth at 0.80c. Determine the round-trip travel times in Earth and ship refer- ence frames.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?
- An astronaut floating in the International Space Station moves at 0.40 m/s to the right. After 5.0sec have passed they are now moving at 1.30 m/s to the left. What was their acceleration duringthis time, stating both the magnitude and direction?(a) A spaceship moves along the x' axis of frame S' with velocity 0.40c. Frame S' moves with velocity 0.60c with respect to frame S. Find the velocity of the spaceship with respect to frame S in unit of e. (b) After the spaceship in (a) travels 1 year in his own frame, how long of the journey with respect to frame S? (c) Given that the mass of 235 U is 235.0429 u, 231Th is 231.0363 u, and *He is 4.0026 u. Where 1 u = 1.66054 × 10-27 kg. Calculate the energy released in the nuclear reaction in unit of Joule, 235 U → 231Th + *He (d) Given elementary charge e = 1.60 × 10-19C. Convert the answer in (c) into unit of eV.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 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 resultsIf relativistic effects are to be less than 1%, then the dimensionless parameter γ must be less than 1.01. At what velocity, in terms of c, is γ = 1.01?