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1. Spatial Separation I

Two firecrackers explode at the same place in the laboratory and are separated by a time of 3 years as measured on a laboratory clock.

A. What is the spatial distance between these two events in a rocket in which the events are separated in time by 5 years as measured on rocket clocks?

B. What is the relative speed of the rocket and laboratory frames?

### 2. Spatial Separation II

Two firecrackers explode in a laboratory with a time difference of 4 years and a space separation of 5 light-years, both space and time measured with equipment at rest in the laboratory. What is the distance between these two events in a rocket in which they occur at the same time?

### 3. Super Cosmic Rays

The Akeno Giant Air Shower Array of detectors spread over 100 square kilometers in Japan detects the energy of individual cosmic ray particles indirectly by the resulting shower of particles these cosmic rays create in the atmosphere. This array has detected a few cosmic ray particles with an energy as high as 1020 electron volts.

A. A regulation tennis ball has a mass of 57 grams. If this tennis ball is given a kinetic energy of 1020 electron volts, how fast will it move, in meters per second? (Hint: Try Newtonian mechanics first.)

B. Research workers find no upper limit on cosmic ray energies. The proposed Pierre Auger Cosmic Ray Observatory will consist of detectors spread over 3000 square kilometers at each of two sites: Utah USA in the northern hemisphere and Argentina in the southern hemisphere. Suppose the new arrays detect a cosmic ray proton of energy 1021 electron-volts, ten times more energetic than those so far observed. How long would it take this proton to cross our galaxy (take the galaxy