This Nuclear Powered Rocket Would Have Been "A Flying Chernobyl"

In 1957, the United States began secretly developing a new type of aircraft. This was the Atomic Age, when nuclear energy seemed to offer unlimited energy in numerous ways. Nuclear reactors provide enormous potential, which is why America put them into submarines and aircraft carriers at this time. It seemed only reasonable to apply this power to aircraft.
Scientists envisioned the Supersonic Low Altitude Missile as a drone that would travel at 2,500 miles per hour over the Earth, dropping multiple hydrogen bombs over the Soviet Union. It would not need to refuel, as conventional aircraft do.
The US had already experimented with putting a nuclear reactor inside a modified B-36 bomber. But the shielding necessary to protect the crew from radiation created weight problems. So developers went in a different direction: a nuclear-powered drone aircraft. Steve Weintz writes for Medium:

While the nuclear aircraft program wrestled with complicated plumbing and tons of shielding, the SLAM project dispensed with the crew and pursued a simple but scary idea—the nuclear ramjet.
A ramjet is a jet engine that moves so fast, the air entering its combustion chamber becomes hot and dense enough to ignite fuel. The resulting explosion of hot gas pushes the ramjet—and its attached vehicle—to supersonic or even hypersonic speeds.
Though simple in design, a ramjet is tough to build and operate. Rockets and conventional turbojet engines must first accelerate a ramjet-powered aircraft fast enough before the ramjet can kick in. Ramjets also require special materials to resist intense heat and pressure. And they gulp fuel like a drag racer.
But if made small, light and tough enough, a nuclear reactor could solve the fuel consumption problem and give a ramjet-powered vehicle enormous range.

It's a great idea. Unless, of course, the nuclear reactor explodes:

Suppose the guidance system failed and a missile roared over friendly territory? If the range-safety officer destroyed it in flight, you still had a supersonic nuclear mess on your hands.
Even if the missile worked as designed, it also violated the recently-signed Atmospheric Test Ban Treaty. An open-cycle engine like the nuclear ramjet exhales radioactive air and dust-sized bits of nuclear fuel as it roars along, and no technology available then or now could clean it up.

Though one scientist who worked on the project described it as "like zany science fiction," the nuclear ramjet soon became obsolete. New intercontinental ballistic missiles could accurately deliver their payloads within minutes--a much shorter period of time than the nuclear ramjet drone offer.