I don't know why I thought of this question but I thought I'd ask to see if someone could help me answer it. My brain wanders a lot and I was actually thinking about noise reduction of an aircraft engine, but this popped out...

Suppose that a single 747 aircraft engine is bolted to some immovable object and operating at full power. Further suppose that a .44 magnum gun is placed at a distance d of 100 meters directly behind the rear exhaust of the engine and fired directly into the center of the rear exhaust. (see more info below)

Factoring only for the thrust and dimensions of the engine, the dimensions and weight of the bullet, and the initial velocity of the bullet, will the bullet reach and/or penetrate the rear exhaust, or will the thrust of the engine "blow" the bullet away before it can reach the exhaust?

Remember, we can take it that there is no gravity and that the bullet is fired in a straight line directly into the middle/center of the exhaust. Any arbitrary or complex factors such as wind (other than the thrust) or vortices within the cone of thrust coming out the back of the engine can also be negated. What I DO want to have included in the calculation is the dissipation of thrust forces as they come out the back of the engine i.e. the thrust force at 3m from the exhaust is not the same as the thrust force at 4m from the exhaust.

Now, I know that a lot depends on the bullet. I'm having trouble finding exact dimensions, but assume a solid point bullet with an initial velocity of 410m/s, a weight of 19g and bullet dimensions of base diameter 11.6mm, tip diameter 10.9mm and length 8mm.

For the engine, I am less certain. It looks like the GEnx-2B engine used on the 747-800 has a maximum thrust of 75,000 lbs. What I don't know about is the rear exhaust dimensions - I would say to calculate just using the assumption of a 1.5-2m diameter rear exhaust, but please feel free to make accuracy adjustments as you see fit.

If the bullet does reach or penetrate the rear exhaust of the engine based on the above info, then how would one calculate a value for d where the bullet exactly reaches the rear exhaust, but does not penetrate?

Sorry for the long and bizarre question, but I hope some of you find it interesting.