ADVANCED DYNAMICS — PHY 4241/5227 HOME AND CLASS WORK – SET 11 (March 12, 2010) (37) 1. Show 1 / √ 1-β 2 = cosh( ζ ). Due March 15 in class (2 points). 2. Show cosh( ζ 2 ) cosh( ζ 1 ) + sinh( ζ 2 ) sinh( ζ 1 ) = cosh( ζ 1 + ζ 2 ). Due March 15 in class (2 points). 3. Velocities are given by β 1 = tanh( ζ 1 ) and β 2 = tanh( ζ 2 ). Use the addition theorem of rapidities to express the velocity given by β = tanh( ζ 1 + ζ 2 ) in terms of β 1 and β 2 . Due March 24 in class (4 points). (38) D mesons have a (mean) lifetime of 1051 × 10-15 s. Assume such a meson is created in a particle collission at Fermilab and moves at 0 . 995 c with respect to the Lab frame. Compute the (mean) distance travelled by such a D meson. Due March 26 before class (6 points). (39) Assume that a rocket ship leaves the earth in the year 2020. The rocket ship is so constructed so that it has an acceleration g in its own frame (to make the occupants feel comfortable). It accelerates on a straight-line path for 5 years
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