Chapter 1, Problem 13P

(a) All but the closest galaxies are receding from our own Milky Way Galaxy. If a galaxy 12.0x109ly away is receding from us at 0.900c, at what velocity relative to us must we send an exploratory probe to approach the other galaxy at 0.990c as measured from that galaxy? (b) How long will it take the probe to reach the other galaxy as measured from Earth? You may assume that the velocity of the other galaxy remains constant. (c) How long will it then take for a radio signal to be beamed back? (All of this is possible in principle, but not practical.)

(a) How fast would an athlete need to be running for a race to look 100 yd long? (b) Is the answer consistent with the fact that relativistic effects are difficult to observe in ordinary circumstances? Explain.

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.)

Joe and Moe are twins. In the laboratory frame at location S1 (2.00 km, 0.200 km, 0.150 km). Joe shoots a picture for aduration of t= 12.0 s. For the same duration as measured inthe laboratory frame, at location S2 (1.00 km, 0.200 km,0.300 km), Moe also shoots a picture. Both Joe and Moe begintaking their pictures at t = 0 in the laboratory frame. Determine the duration of each event as measured by an observer ina frame moving at a speed of 2.00 108 m/s along the x axisin the positive x direction. Assume that at t = t = 0, the origins of the two frames coincide.

(a) Does motion affect the rate of a clock as measured by an observer moving with it? (b) Does motion affect how an observer moving relative to a clock measures its rate?

Two atomic clocks are synchronized. One is placed on a satellite which orbits around the earth at high speeds for a whole year. The other is placed in a lab and remains at rest with respect to the earth. You may assume both clocks can measure time accurately to many significant digits. a)Will the two clocks still be synchronized after one year? b) imagine the speed of light is much lower than its actual value. How would the results of this experiment change if the speed of light was only twice the average speed of the satellite? Explain your reasoning using a calculation.

In the movie Interstellar, the main characters are on a planet where 1 hour = 7 years on Earth. If you are 30 years old on Earth how many hours have passed by on the planet?

Assume your hair grows at a rate of 1/44th of an inch per day. How fast is that in nm/s (nanometers per second)? Given that a typical atom is on the order of 1 x 10^(-10) m in diameter (see Table 1.3 on page 18 of the textbook), at approximately what rate does the protein synthesis that assembles your hair strands deposit atoms in units of atoms per second? I need the second question to be rounded to 1 significant digit.

Tony & Yuki are working at a particle linear accelerator  that is  414 meters long.  A particle is moving at 0.89 c in the  accelerator.  What is the length of the  particle accelerator in meters according to the particle?  Give your answer with no decimal places please.