Jack Waid
Is there a linkage between jets and missiles? Yes, there is, and it is in the engine technology! The linkage specifically begins with the Allison J33 turbojet engine, originally installed in the Lockheed F-80, and is woven together through the Snark glide missile system which incorporated jet engine and nuclear technologies leading the United States into the post-World War II nuclear age.
The evolution of missile technology after World War II allowed missiles to be suitable for an increasingly wide range of missions, specifically to carry a nuclear payload. In August 1945, the Army Air Forces (AAF) established a requirement for a 600 mph, 5,000-mile-range missile, with a 2,000-pound warhead. (The warhead/payload requirement was veiled in secrecy, this due to the secretive nature surrounding nuclear weapons.) In response, Northrop developed the MX-775A (DoD designation)/N-25 (Northrop designation) – Northrop Snark, which is today considered an antecedent of our contemporary Intercontinental Ballistic Missile arsenal.
A Northrop Snark missile in flight. 
An individual installs an Allison J33 engine inside of a F-80. 
An Allison J33 engine on display.