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# relativity problem

Dear Stanley,

Let b=v/c = 0.95 and a=1/sqrt(1-b^2) = 3.2026 and l = 200 m, the proper
length of the ship.

Then there are two ways to get the right answer:

Method A: simple physics in the earth frame
Method B: the Lorentz transformations.

Method A: A spaceship of length l'=l/a travels a distance vt while the
light beam travels a distance ct = vt + l'. Solve for t.

Method B: x = a(x'+ vt') and t = a(t'+ vx'/c^2) are the Lorentz
transformations from the ship frame to the earth frame. Let the tail of the
ship be at x'=0 at t'=0. and interpret the above equations as space and
time *intervals*. Accordingly set x' = 200 and t' = l/c, and solve for t.

Both methods give 4.16 micoseconds. You're right, the book is wrong.

Vince

Vince Santarelli santarel@andromeda.rutgers.edu
Physics Department, Smith Hall, Rm.366 OFFICE: (201) 648-5072
Rutgers University, Newark Campus DEPT: (201) 648-5250
Newark, NJ 07102 FAX: (201) 648-1434