A shaped charge anti$-$tank weapon with copper $($density: $8960k\frac{g}{m^3})$ liner was fired

towards a heavily armoured vehicle. A rod like jet with a length of $200$ mm impacts

the composite armour that comprises $20$ mm thick tungsten $($density: $19300$ kg $/$

$m^3),60$ mm thick steel $($density: $7850k\frac{g}{m^3}),20$ mm thick aluminium $($density$.$

$2700k\frac{g}{m^3}),$ and $20$ mm titanium $($density: $4510k\frac{g}{m^3}).$ The tip of jet is travelling

at $5\mathrm{.}9k\frac{m}{s}.$ Assuming that one$-$dimensional penctration and all materials are

strengthless, what is the length of the jet that perforated the armour and flied into

the vehicle?