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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 straightline path for 5 years
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 Spring '11
 Berg
 Work

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