Consider some inertial observers S, S' and S" in the standard configuration and such that observer S' has velocity v₁ with respect to S, whilst S" has velocity v₂ with respect to S'. Then, according to the Newtonian Framework (i.e., using Galilean transformations), the velocity of S" with respect to S is: Select one: O a. - V₁ + V₂ O b. V₁+2 V₂ OC. V₁ V₂ O d. V₁ + V₂
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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.) |cIf ever the human race would need to leave Earth, the Trappist-1 system might make a good destination – the star there has seven temperate terrestrial planets, a few of which are close to Earth’s size and mass. It’s 39.6 light years away, though, so it could take a long time to get there. (a) If the spaceship had a speed of 0.95c, how long would the journey take from the Earth’s reference frame? (b) How long would the journey be for the passengers on the spaceship?1) Calculate the interval As 2 between two events with coordinates (x1 = 50 m, y1 = 0, z1 = 0, t1 = 1 us) and (x2 = 120 m, y2 = 0, z2 = 0, t2 = 1.2 µs) in an inertial frame S. 2) Now transform the coordinates of the events into the S0 frame, which is travelling at 0.6c along the x-axis in a positive direction with respect to the frame S. Hence verify that the spacetime interval is invariant.
- The spaceship Lilac, based on the Purple Planet, is779 m long when measured at rest. When the Lilac passes Earth, observers there measure its length to be 724 m. At what speed v is the Lilac moving with respect to Earth? Express your answer as a multiple of the speed of light ?.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.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?
- For the twins Frank and Mary described in Section 2.8, consider Mary's one-way trip at a speed of 0.8c to the star system 8 lightyears from Earth. Compute the spacetime interval As? in the fixed frame and As'2 in the moving frame and compare the results.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 XmYou and vouur archenemy pass each other in rockets that are each traveling 0.2c relative to the other. You observe that your rocket (which you have measured to be 281 m Jong ten times as long as your archenemy's spaceship. How long is your rocket in your archenemy's frame? How long is your archenemy's rocket in their frame?