An armada of spaceships that is 1.00 ly long (as measured in its rest frame) moves with speed 0.800c relative to a ground station in frame S.A messenger travels from the rear of the armada to the front with a speed of 0.950c relative to S. How long does the trip take as measured (a) in the rest frame of the messenger, (b) in the rest frame of the armada, and (c) by an observer in the ground frame S?

As spaceship A moves away from the earth at 0.510c, the captain observes a second spaceship (B) moving in the same direction at a speed of 0.520c relative to A. Find the speed of B relative to the earth.

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.

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 4.60e+05 m. How much time does Quicksilver measure this trip as taking? 2.73e-3 S Does Quicksilver measure the proper or dilated time? 2 proper time v Quicksilver's sister, Wanda Maximoff, is standing stationary near where he is running. How much time does Wanda measure this trip as taking? 3 3.29e-3 S What distance does Wanda measure for Quicksilver's trip? 4 Xm

A person on Earth observes two rocket ships moving directly toward each other and colliding as shown in the figure below. At time t = 0 in the Earth frame, the Earth observer determines that rocket A, travelling to the right at vA = 0.80c, is at point a, and rocket B is at point b, travelling to the left at vB = 0.60c. According to the Earth observer they are separated by a distance l = 4.2 x 108 m as shown in the other figure. How much time will elapse in frame A from the time rocket A passes point auntil collision?

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?

The inertial reference frames, S and S', both share the same origin at t =t'=0. The S' frame is moving at a speed 0.700c in the positive direction, as seen by frame S. An event happens at (t',x', y', z') (300s, 2.50x10"m, 1.50x10"m, 2.90x10"m), as observed in the S' frame. What are the spacetime coordinates in the S frame?