ROSAT observations of the Vela pulsar and its surroundings revealed a collimated X-ray feature almost 45 \arcmin in length ( Markwardt & Ögelman 1995 ) , interpreted as the signature “ cocoon ” of a one-sided jet from the Vela pulsar . We report on a new ASCA observation of the Vela pulsar jet at its head , the point where the jet is believed to interact with the supernova remnant . The head is clearly detected , and its X-ray spectrum is remarkably similar to the surrounding supernova remnant spectrum , extending to X-ray energies of at least 7 keV . A ROSAT+ASCA spectrum can be fit by two-component emission models but not standard one-component models . The lower energy component is thermal and has a temperature of 0.29 \pm 0.03 keV ( 1 \sigma ) ; the higher energy component can be fit by either a thermal component of temperature \sim 4 keV or a power law with photon index \sim 2.0 . Compared to the ROSAT-only results , the mechanical properties of the jet and its cocoon do not change much . If the observed spectrum is that of a hot jet cocoon , then the speed of the jet is at least 800 km s ^ { -1 } , depending on the angle of inclination . The mechanical power driving the jet is \geq 10 ^ { 36 } erg s ^ { -1 } , and the mass flow rate at the head is \geq 10 ^ { -6 } M _ { \sun } yr ^ { -1 } . We conclude that the jet must be entraining material all along its length in order to generate such a large mass flow rate . We also explore the possibility that the cocoon emission is synchrotron radiation instead of thermal .