Thanks for the video.
So, the kinetic energy generated by the fired projectile acts against the forward movement of the aircraft? Let's look at the numbers.
The A-10 Thunderbolt II has an average loaded weight of 42,000 pounds (as listed on Wikipedia for anti-armor missions). At 340 mph (cruise speed, approx. 500 fps), this translates into about 163.2 million foot-pounds of energy (Weight in grains times velocity in fps squared divided by 450,240).
The GAU 8/A generates approximately 178,482 foot-pounds of energy with each shot (6560 grain projectile at 3500 fps). This is about 0.00109 the kinetic energy of the aircraft. Added together, this makes a 1 second burst (65 rounds) from the GAU 8/A about 11.6 million foot-pounds, or about 0.071 the kinetic energy of the aircraft.
So according to my calculations (please check my math), a one second burst from the cannon translates into a 7.1% loss in the forward velocity of the aircraft. One can presume longer bursts have a greater effect, but at some point the continued thrust of the engines would have to mitigate the effect of the cannon.
I should have crunched the numbers first and saved myself the embarrassment.