A rocket is to travel from Earth to a nebula 5.45 ly away. At what speed must the rocket travel in order for the Earth–nebula distance to be 3.20 ly, when measured in the reference frame of the rocket? Express your answer as a multiple of c, the speed of light in a perfect vacuum.

My question is about special relativity. Three interconnected rods form a 90-45-45 triangle that reside on the plane x′y ′ of frame O. The chord of this triangle is in the direction of the x-axis. The frame O in the x direction moves away from the frame O at a speed of 0.6c. What are the angles of this triangle from the observer O's point of view (in degrees)?

Suppose an astronaut travels to a star 10 lightyears away at a significant fraction of the speed of light (for example, v=0.99c) and returns. Assume negligible amount of time is spent at the destination. Does this round-trip journey take less than, equal to, or more than 20 years as observed by an Earth-based observer? Does this round-trip journey take less than, equal to, or more than 20 years as observed by the astronaut?

In the Marvel comics universe, Quicksilver is awfully fast. Let's say he can run at a velocity of 0.56c. He measures a trip as having a distance of 4.19e+05 m. How much time does Quicksilver measure this trip as taking? Does Quicksilver measure the proper or dilated time? Quicksilver's sister, Wanda Maximoff, is standing stationary near where he is running. How much time does Wanda measure this trip as taking? What distance does Wanda measúre for Quicksilver's trip?

4.3 Time dilation for a biological clock. I trim my moustache every 6 weeks. If I were in a rocket ship flying past you at a speed of V=c, then how much time, in your frame, would elapse between my moustache trimmings? 44 Munn lifetime. The lifetime of a stationary muon is 2.2 microseconds. A beam of

(a) Enterprise spaceship is flying towards a star at velocity of 0.80c. Light emitted from the star is traveling in opposite direction of the Enterprise's velocity. What is the speed of the light measured from the frame of Enterprise? Based on what postulate you get your answer? (b) Captain Kirk is doing an elastic collision experiment in zero-g environment on Enterprise which is traveling at velocity of 0.80c with respect to Earth. Captain Kirk measured the initial momentum of the system is p; and the momentum after collision is pr. To an observer on Earth, he measured the correspoding initial and final momentum denoted as p' and p'. Is p = p:' ? (Answer yes or no and provide reasons). (c) If Captain Kirk obtained pf – P; = 0, will the observer on Earth also conclude the same result p;' – p;' = 0? (Answer yes or no and provide a justification.) (d) Captain Kirk throws a wrench in zero-g environment. The wrench rotates naturally around its center of mass.(Figure 3) Explain why does the…

A light source G is moving, with respect to an observer O, at an angle θ=�=154∘∘ between the direction of relative motion and the line of sight from O to G. The redshift of the light emitted by G and measured by O is z=0�=0. Find the speed of G with respect to O in units of c�, the speed of light. Enter your answer to 3 decimal places.

In frame S, event B occurs 2 ms after event A and at Dx = 1.5 km from event A. (a) How fast must an observer be moving along the +x axis so that events A and B occur simultaneously? (b) Is it possible for event B to precede event A for some observer?(c) Draw a spacetime diagram that illustrates your answers to (a) and (b). (d) Compute the spacetime interval and proper distance between the events.

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.) |c

Imagine a spaceship approaching Earth at speed v=(0.75c) c, which sends a message capsule toward Earth at speed 0.1 00c (relative to the ship). Calculate the speed of the capsule relative to Earth in terms of c.