Rescuing a child in a runaway balloon like the one that soared over Colorado today is nearly impossible.
Unlike an airplane, a balloon doesn't travel forward through the air. Instead, it floats with the wind, with an airspeed of zero. Even the slowest-flying airplane would zoom past the balloon.
Although a helicopter could match the balloon's speed, the downwash from the helicopter's rotors could blow the balloon apart.
(The risks posed by helicopter downwash to ultralight vehicles were tragically illustrated by the death of hang gliding champion Bob Wills, who was killed in 1977 when a helicopter flew above him during the filming of a Jeep commercial, throwing his glider out of control.)
One of the few theoretical rescue options is to dispatch an airship like the Goodyear blimp, which could float in formation with the balloon. In reality, it would be extremely difficult to precisely match the balloon's buoyancy and keep the blimp at the same level, and reaching the child inside might be impossible.
A helium balloon develops lift because the gas inside its envelope is lighter than the surrounding air. As it rises, the gas expands due to decreasing atmospheric density. A helium balloon also responds to changing temperature - strong sunlight heats the gas inside, making the balloon rise. As the sun sets, the gas cools, and the balloon begins to descend.
How high a balloon climbs depends on its ratio of lift to weight - the bigger the balloon and the lighter the cargo, the higher it can climb.
Gas balloons have been used to make a long series of record flights. In 2002, adventurer Steve Fossett flew a gas balloon around the world. The gas balloon altitude record is 34,668 meters, set in 1961 by pilot Malcolm Ross over the Gulf of Mexico.