A)How do the clock readings change as you vary the x position of the viewer? B)How do the clock readings change as you vary the z position of the viewer?C)Where does a viewer need to be located for the clocks to appear synchronized?

A spacecraft built in the shape of a sphere moves past an observer on the Earth with a speed of 0.500c. What shape does the observer measure for the spacecraft as it goes by? (a) a sphere (b) a cigar shape, elongated along the direction of motion (c) a round pillow shape, flattened along the direction of motion (d) a conical shape, pointing in the direction of motion

If astronauts could travel at v = 0.950c, we on Earth would say it takes (4.20/0.950) = 4.42 years to reach Alpha Centauri, 4.20 light-years away. The astronauts disagree. (a) How much time passes on the astronauts clocks? (b) What is the distance to Alpha Centauri as measured by the astronauts?

Two powerless rockets are on a collision course. The rockets are moving with speeds of 0.800c and 0.600c and are initially 2.52 × 1012 m apart as measured by Liz, an Earth observer, as shown in Figure P1.34. Both rockets are 50.0 m in length as measured by Liz. (a) What are their respective proper lengths? (b) What is the length of each rocket as measured by an observer in the other rocket? (c) According to Liz, how long before the rockets collide? (d) According to rocket 1, how long before they collide? (e) According to rocket 2, how long before they collide? (f) If both rocket crews are capable of total evacuation within 90 min (their own time), will there be any casualties? Figure P1.34

Choose the option from each pair that makes the following statement correct. According to an observer at rest, moving clocks run more [(a) slowly; (b) quickly] than stationary clocks and moving rods are [ (c) longer; (d) shorter] than stationary rods.

A clock on a moving spacecraft runs 1 s slower per day relative to an identical clock on Earth. What is the relative speed of the spacecraft? (Hint: For v/c << 1, note that γ ≈ 1 + v2/2c2.)

If astronauts could travel at v = 0.950c, we on Earth would say it takes (4.20/0.950) = 4.42 years to reach Alpha Centauri, 4.20 light-years away. The astronauts disagree. (a) How much time passes on the astronauts clocks? (b) What is the distance to Alpha Centauri as measured by the astronauts?

An alien spaceship traveling at 0.600c toward the Earth launches a landing craft. The landing craft travels in the same direction with a speed of 0.800c relative to the mother ship. As measured on the Earth, the spaceship is 0.200 ly from the Earth when the landing craft is launched. (a) What speed do the Earth-based observers measure for the approaching landing craft? (b) What is the distance to the Earth at the moment of the landing crafts launch as measured by the aliens? (c) What travel time is required for the landing craft to reach the Earth as measured by the aliens on the mother ship? (d) If the landing craft has a mass of 4.00 105 kg, what is its kinetic energy as measured in the Earth reference frame?

Suppose an astronaut is moving relative to the Earth at a significant fraction of the speed of light. (a) Does he observe the rate of his clocks to have slowed? (b) What change in the rate of Earth-bound clocks does he see? (c) Does his ship seem to him to shorten? (d) What about the distance between stars that lie on lines parallel to his motion? (e) Do he and an Earth-bound observer agree on his velocity relative to the Earth?

(a) How long would the muon in Example 28.1 have lived as observed on the Earth if its velocity was 0.0500c ? (b) How far would it have traveled as observed on the Earth? (c) What distance is this in the muon's frame?