## A Perplexing Problem

Let's say that you are traveling along at about 300 km/h. For some reason, you decide to do some target shooting in order to pass the time. You take out your trusty gun (or cannon or what-have-you), and you point it backward. In this case, you are firing in the opposite direction that you are traveling (after all, you don’t want to shoot the conductor).

As luck would have it, your weapon fires at the exact same speed that you are traveling. So, you are flying along at 300 km/h and you are about to shoot a bullet/cannon/whatever in the opposite direction at 300 km/h. What happens to the projectile?

What happens to the projectile? Does it go shooting off in the opposite direction? Does it go anywhere?

At first glance, this may seem like a silly question. After all, what are the chances that a bullet will travel at the exact same speed that you are? When you think about it, in reality, the odds are rather slim. However, the question is actually rather important, as it is something that engineers have to take into consideration when designing any aft firing aircraft.

Of course, in the real world, there are a few different ways that this could play out (depending on the specific conditions); however, the short answer can be derived as follows:

• You are traveling along a path at 300 km/h. We will call this +B
• You fire in the opposite direction at 300 km/h. We will call this -B
• So you are traveling at +B and you fire at –B. This equals zero
• So the bullet should fall straight down.

That’s right. If you are traveling at the speed of a bullet and fire backward, the projectile plummets straight down.

What would this look like? For an onlooker, someone who is standing still and watching you as you pass by, they will see you take aim and pull the trigger; however, the bullet leaving the weapon will appear to fall straight down as the train pulls away from around it (I am assuming that the back of the train is open, and that the observer is located at a space where they can clearly see all of this happen).

But as I mentioned earlier in reality, things are a bit more complicated. First, even if the projectile can travel 300 km/h in the opposite direction (the exact same speed that you are traveling), it will need a bit of time to reach that speed. In short, when you pull the trigger, the bullet won’t immediately be traveling at 300km/h in the opposite direction (-B). So since the bullet takes time to accelerate, when you pull the trigger, the bullet in the chamber will have to speed up to reach –B and cancel out the effects of B. So in reality, the projectile would not fall straight down as soon as you pull the trigger.

The short answer also assumes that there is no air resistance. And of course, there will be air resistance. Moreover, in a gun, rifle, or similar weapon, the projectile will spin. Both the air resistance and spin will cause the projectile to go off course a bit. In other words, it won’t go back perfectly straight, and will end up shooting off course a bit (which means no falling straight down). That said, assuming that you just want the projectile to fall straight down, it is possible to get the projectile to do this – it is just exceedingly hard as the conditions have to be nearly perfect. Unfortunately, I don’t have the time to establish perfect conditions…but others did. To see this in action, check this video:

Along these same lines, if you shoot forward at 300 km/h, then the projectile will be moving forward at 600 km/h relative to the ground (again, this is not taking any contributing factors into consideration).