ADVANCED DYNAMICS — PHY 4241/5227

HOME AND CLASS WORK – SET 9

(March 29, 2010)

(26) Exercises with the rapidity variable.

1. Show 1/\sqrt{1 − β^{2}} = cosh(ζ). Due in class (2 points).

2. Show cosh(ζ_{2}) cosh(ζ_{1}) + sinh(ζ_{2}) sinh(ζ_{1}) = cosh(ζ_{1} + ζ_{2}). Due 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 in class (4 points).

(27) 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 April 4 before class (6 points).