Consider the decay Λ^{0} --> n + π^{0}, followed by π^{0}
--> 2γ.

(a) Given the masses M_{Λ}, M_{n} and M_{π}, find the
energy of the decay products n and π^{0} in the rest frame of the Λ^{0}.

(b) The two gamma rays from the decay of the π^{0} are observed to have
equal energies in the rest frame of the Λ^{0}. Find the angle between
the two gamma rays in this frame, in terms of the particle masses.

As a rocket ship passes Earth at speed (3/5)c, clocks on Earth and on the
ship are synchronized at t = 0. The rocket ship sends a light signal back to
Earth when its clock reads one hour.

(a) According to Earth's clock, when was the signal sent?

(b) According to Earth's clock, how long after the rocket passed did the signal
arrive back on Earth?

(c) According to the ship clock, when did the signal arrive back on Earth?

An entrepreneur decides to operate a spacewash, which is normally at rest
relative to its home planet. Although the device is only 100 meters long, he
advertises the spacewash as "the only one that simultaneously washes the front
and back of a WizzFlizz 200TM". According to the catalog, the WizzFlizz 200TM
is 200 meters long.

(a) An inspector arrived at spacewash to check how it operates. What is the
minimum speed v_{0} (in units of c) at which the WizzFlizz 200TM must go
through the spacewash for the advertisement to be true? (Assume that the wash
is instantaneous.)

(b) The pilot of the WizzFlizz 200TM observes the wash process from the
spaceship. At the minimum speed v_{0}, how accurate does the pilot's
clock need to be to see that the simultaneity claim is false? (Assuming that
it's true if observed from the spacewash.)

(c) Suppose a spaceship is approaching the home planet with insufficient
speed (4/5)v_{0}. The spacewash has its own engine that allows it to
accelerate toward the ship. To what speed should it accelerate (relative to its
home planet) to perform the wash as promised in the advertisement?

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?

A relativistic particle is launched at the origin (0,0) with initial momentum
**p**(0) = (p_{x}(0), p_{y}(0)), with p_{x}(0)
> 0 and p_{y}(0) > 0, and is subject to a
constant force pointing in the negative y direction.

(a) Solve the
equations of motion for x(t) and y(t).

(b) Determine the time T at which the particle reaches the x-axis
again (i.e. y(T) = 0).

(c) Find the trajectory of the particle, i.e. y = y(x).

NOTE: Give all answers for the laboratory frame.