We examine the constraints imposed on the total kinetic power ( L _ { j } ) and the age ( t _ { 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 _ { j } and t _ { age } .
The estimate of L _ { j } and t _ { 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 { Myr } < t _ { age } < 30 { Myr } and ( ii ) the total kinetic power of the jet is estimated as 0.2 \times 10 ^ { 46 } { erg s ^ { -1 } } < L _ { j } < 1 \times 10 ^ { 48 } { erg s ^ { -1 } } which is larger than 1 \% of the Eddington luminosity of Cygnus A .