Assignment 7

Problem 1:

The 21 cm line (1420.4 MHz) line of neutral hydrogen atoms from a gas cloud is monitored with a radio telescope on Earth.
(a)  If the distance galaxy is moving with speed 0.2c perpendicular to the line of sight, what will be the observed frequency?
(b)  If the distant galaxy is receding with speed 0.2c along the line of sight, what will be the observed frequency?

Problem 2:

Two spaceships, each measuring 100 m in length in its own rest frame, pass by each other traveling in opposite directions.  Instruments on spaceship 1 determine that the front end of spaceship 1 requires (5/3)*10-7 s to traverse the full length of spaceship 2.  What is the relative speed of the two ships?

Problem 3:

A beam of antiprotons is incident on a hydrogen target at rest.  In a proton-antiproton reaction, a lambda particle and an anti-sigma particle are produced.
p(bar) + p --> Λ + Σ0(bar).
(a)  What is the minimum kinetic energy of the antiproton to make this reaction possible.
(b)  What is the velocity of the reaction products right after the collision?
The rest masses are mp(bar) = mp = 938.27 MeV/c2, mΛ = 1115.68 MeV/c2,  mΣ0(bar) = 1192.64 MeV/c2

Problem 4:

In inertial frame O a rod of length L is oriented along the x-axis and moving with velocity u in the positive y direction.  This rod is then viewed from an inertial reference frame O' moving with velocity v in the positive x direction.
(a)  What is the velocity of the rod in O'?
(b)  What is the length of the rod in O'?
(c)  What angle does the rod make with respect to the x' axis?

Problem 5:

An observer moves horizontally away from a flashlight with a speed 0.6c. 
(a)  The flashlight is pointed in the direction of the observer and emits light.  Prove that the speed of the light determined by the observer is exactly c. 
(b)  The flashlight is now turned perpendicular to the direction of motion for the observer and light is emitted.  Demonstrate that the observer again will deduce that the speed of the light as measured in her frame is c.
(c)  What angle will the light velocity vector make with the horizontal axis in the observer's frame for case b?