When an object approaches the speed of light, we observe several things. Which of the following is not correct? it becomes more massive. it becomes shorter in each of its dimensions. its momentum approaches infinity. its rest mass remains constant. its time slows down.

8. Adam and Avani are twins. On their 19th birthday, Avani leaves on a spaceship and travels at 0.80 c. Avani returns to Earth on the day that Adam is celebrating his 35th birthday. How old does Avani believe she is?

4. Relativistic Doppler shift: A spaceship with speed v close to c is moving away from Earth. At regular intervals of time, At', (as measured in the ship's frame), it sends out a light pulse. (a) In the inertial reference frame in which Earth is at rest, give the equation for the time interval between successive pulses being emitted? (b) In the inertial reference frame in which Earth is at rest, what give the equation for the time interval between successive pulses arriving at Earth? Give the answer in terms of v, c and At'. (c) If we convert the arrival time interval into a frequency, via f = 1/At, show that 1 - fs, farrival 1+v/cs» where f = 1/Ať. (This is the formula for the relativistic Doppler shift, by which the light from distant galaxies, moving at relativistic speeds away from us, is red-shifted.) (d) Use the formula from part (c) to find the speed v at which blue light with frequency 650 x 1012 Hz, emitted by the spaceship, will be received on Earth as red light with…

1. A spaceship A (at rest in inertial frame A) of proper length L, =75.0m is moving in the +x direction at a speed v= 0.650c as measured in the Earth frame. Another spaceship B (at rest in inertial frame B) is moving on a parallel path in the opposite direction (-x) with u, =-0.720c as measured in the Earth frame. The two spaceships pass each other. a. What is the velocity and speed parameter of spaceship B in inertial frame A, u,,B' ? b. In inertial frame A, how long does it take for the tip of spaceship B to move from the tip of spaceship A to the tail of spaceship A? c. In inertial frame B, how long does it take for the tip of spaceship B to move from the tip of spaceship A to the tail of spaceship A? d. In the Earth frame, how long does it take for the tip of spaceship B to move from the tip of spaceship A to the tail of spaceship A?

John, in his spaceship, observes as Sally, in her spaceship, passes him at a speed of v=0.8c. John who was born and raised on his spaceship, is 20 years old. According to Sally, how old is he? How many birthday parties should he have had and how many presents should Sally have sent him?

1. You are an observer in a 100-m long spacecraft traveling from the earth to the moon at 0.8c. (a)What is the proper length of the spacecraft? (b) For a proper time interval of 1 sec., the relativistic time interval for the spacecraft measured from the earth reference frame would be: (c)Time dilation does not apply to all time-dependent physical and biological processes. T/F? (c) What is the relativistic length, DL measured from the reference frame of earth? (d) An APOLLO crew left a flat mirror reflector on the surface of the moon (for all you deniers out there, in the 50th anniversary year of APOLLO 11!). If the average surface-to-surface distance from the earth to the moon is 3.83 x 10^8 m, then how long does it take moonlight to reach earth?

How fast is a rocket going it its passengers measure its length to be 25.5 but the people on earth watching it go by measure its length to be 18.8? Please give your answer as a fraction of c. For example, if v=1.5*10^ 8 m/s,use V/c=0.5 .

6. A particle has a speed of 96% of the speed of light and a mass of 1u. The particle is unstable and its lifetime is 150 ns. It passes through a room where we stand and observe.   (a) How long do we think the lifetime of the particle is?   (b) The room is 10 m long, but how far does the particle feel as it passes?  (c) How much of the particle's total energy is rest mass?

The speed of light relative to still water is 2.25 * 10^8 m/s. If the water is moving past us, the speed of light we measure depends on the speed of the water. Do these facts violate Einstein’s second postulate? Explain.

Suppose 5 rocketships are all traveling in â in some frame S. The speeds are: St (min) 100 B 0 0.25 0.5 0.75 0.99 7 1 How much time passes on the clocks inside each rocketship if 100 minutes elapse on the stationary rocketship?