Starting from the Lorentz transformation, derive time dilation ?t = ? ?t0. Sketch the situation, defining all of the variables.

a) Find the value of y for the following situation. An astronaut measures the length of his spaceship to be 100 m, while an earthbound observer measures it to be 25 m. b) What is the speed of the spaceship relative to Earth?

Please answer D A spaceship from another galaxy passes over the solar system directly above a radial line from the sun to the Earth. (We measure the distance between the Earth and the Sun to be 1.496 x 1011 m.) An observer standing on the Earth measures that the spaceship is approaching at 0.800c. The Earth-based observer also measures that it takes the spaceship 625 seconds to travel from the sun to Earth. Ignore the relative motion of the Sun and Earth in this problem – their relative speed is only 0.001c, negligibly small compared to 0.800c. a) According to a scientist in the spaceship, the Earth-Sun distance is: 8.976 x 1010m b) According to a scientist in the spaceship, the time it takes her to travel the Earth-Sun distance is: 357s c) What is the ratio of the kinetic energy to rest energy of the spaceship? KE/ER = 0.667 d) As the spaceship passed over the Sun, the alien scientist launched a probe toward Earth, traveling at 0.200c relative to the spaceship. What would the…

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