hw1_assignment - PHY 251 Fall 2009 homework problem set 1...

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PHY 251 Fall 2009: homework problem set 1, due PHY 251 drop box in room A-129 by noon on Friday, Sep. 11. 1. Show that if one uses the Galilean relativity transformation of x 2 = x 1 vt 1 y 1 = y 2 z 1 = z 2 t 1 = t 2 (1) and the relationships for expansion of light spheres of x 2 1 + y 2 1 + z 2 1 c 2 t 2 1 = 0 (2) x 2 2 + y 2 2 + z 2 2 c 2 t 2 2 = 0 . (3) that you get a non-general and inconsistent-with-classical-physics result. 2. Show how classical relativity affects speed in an airplane flight with either headwinds and tailwinds, or crosswinds. Let’s say that the wind is blowing east west at a velocity of v = 10 m/s, and that you’re in an airplane that travels at a speed of c = 250 m/s. Consider a round- trip journey where you fly 300 km out and back as measured on the ground, going east then west. Then consider the case where you go straight south then north as measured from the ground (what compass heading should you fly the plane at to accomplish this?). What’s the time difference between the two trips? Work out an algebraic answer approximated to lowest
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