Physics with Richard Bleil
Recently the Sheriff’s department in South Carolina issued a public plea for citizens to avoid shooting at the Chinese spy satellite currently crossing the US. Now, personally, I don’t understand the concern with the balloon. What is it going to find that satellites cannot? I guess that since it is inside the atmosphere it can pick up sounds, but why the concern? And besides, isn’t this a great opportunity to feed China a boatload of false and confusing information to force them to spend resources to discover nothing? I also know that the US has been developing lasers with defensive (or offensive) capabilities. Isn’t this a great opportunity to try out some of those prototypes, whether or not they’re ready? Plus, with a laser, there’s no risk of slugs falling back to earth potentially causing damage, harm or even death?
And therein lies the problem. The ignorant gun owners who see this as a “patriotic opportunity” to fire their phallic symbol guns are probably too poorly educated to understand that the slugs will return to the earth. While the odds of hitting something are very small, it’s not zero. But the question then becomes, can they even reach the balloon with the weapons they hope will divert questions about the sizes of their collective penises?
Currently, the balloon is flying somewhere around 60,000 ft. Acceleration due to gravity is 32 ft/s^2. The (algebraic) formula for distance of an object with acceleration is d=vt+0.5at^2, where d is distance, v is velocity, t is time and a is acceleration. The initial velocity, of course, would be related to muzzle velocity. Let’s assume that the greasy gun owner shoots straight up, so accurately, in fact, that the bullet will fall straight back down and hit him in his crusty oversized butt. By making this assumption, we can ignore the idea of vectors, which would bleed some of the velocity away. For example, at a 45o angle (the optimal angle for maximum distance for the bullet to travel), literally half of the muzzle velocity goes towards horizontal initial velocity instead of vertical. And for those idiots shooting guns at the balloon, “vertical” means towards the sky, and “horizontal” means towards your cousin’s and brother-in-law’s house.
Okay, let’s address something here. I’m getting a lot of enjoyment poking fun at these gun toting morons shooting at the balloon. I am a gun owner myself, and I don’t want this to be taken as a general denigration of gun owners in general. I’m really poking fun at the idiots who see this balloon as an opportunity to finally shoot at something other than a paper target. Indiscriminately shooting a gun into the air, even at a spy balloon, is inherently idiotic, and anybody doing so should lose their right to even own a gun, and should certainly be held accountable for any damage or harm they cause, up to and including manslaughter. Or, even if the slug doesn’t cause harm, perhaps attempted manslaughter anyway.
Okay, we still need time. That would be the time it would take the bullet to rise 60,000 ft just to kiss the balloon, but probably not with enough force to bring it down. There’s a beautiful symmetry in physics that we frequently see. If we ignore wind resistance (which in reality we cannot, so this is just an academic exercise), the time it would take a bullet to reach the balloon would be exactly equal to the time it would take for the bullet to fall back to earth. This let’s us ask the question, suppose we simply dropped the bullet from the balloon. How long to fall onto our intellectually challenged shooter’s head? The distance we know, and acceleration is 32 ft/s^2. The formula is d=0.5at^2, or 60,000=0.5*32*t^2. We have one and only one unknown (t), so when we do a little bit of algebra, we discover that t is 61.2 seconds, or a little over a minute. Of course, the actual time would be longer, but we’ll start with this.
Now, we have time, acceleration and distance (height), so using the formula d=vt*0.5t^2, we can solve for the minimum muzzle velocity that we need to reach the balloon by solving the formula 60,000=v(61.2)+0.5(-32)(61.2)^2. The astute reader will notice that I’ve changed the sign for acceleration basked on the above equation. This is because, as we shoot against gravity, the gravity will be decelerating our bullet, rather than accelerating. Solving for v, we get an necessary muzzle velocity of 1,960 ft/s. Now, keep in mind that this is under ideal and vacuum conditions, so the actual muzzle velocity will need to be greater, perhaps significantly so.
The answer, then, is yes, the bullet can reach the balloon if shot straight up. The AR-15 has a muzzle velocity of 3,300 ft/s, but any angle less than about 45o wouldn’t have enough vertical velocity to reach it. If they were shooting a handgun, say a .45, depending on the ammo used, the maximum muzzle velocity is around 1,300, so that wouldn’t even reach the balloon under any circumstances. The 9mm is a very popular handgun, but this muzzle velocity is no better. An AK-47 would reach, with a muzzle velocity of about 2,300 ft/s, but a shotgun maximum muzzle velocity is 1,300 ft/s and could never reach. So assault rifles would reach it, but only if shot very nearly straight up, but not handguns or most other rifles. In other words, PUT YOUR DAMNED GUNS AWAY! The military has got this.
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