  We examine the constraints imposed on the total kinetic power ($L_{\rm j}$)
and the age ($t_{\rm age}$) of relativistic jets in FR II radio sources in a
new way. We solve the dynamical expansion of its cocoon embedded in the
intra-cluster medium (ICM) and obtain the analytic solution of its physical
quantities in terms of $L_{\rm j}$ and $t_{\rm age}$. The estimate of $L_{\rm
j}$ and $t_{\rm age}$ is done by the comparison of the model and the observed
shape of the cocoon. The analysis is focused on Cygnus A and we find that (i)
the source age is $3 {\rm Myr} <t_{\rm age}<30 {\rm Myr}$ and (ii) the total
kinetic power of the jet is estimated as $0.2\times 10^{46}{\rm erg s^{-1}}
<L_{\rm j}<1\times 10^{48} {\rm erg s^{-1}}$ which is larger than 1% of the
Eddington luminosity of Cygnus A.
