Vector problems can be resolved graphically and are very intuitive that way. Before calculators graphic methods were extensively used. Navigation used graphic methods well after WWII.
Still does. The wind side of a so-called flight computer or “whizz-wheel” is a graphical technique for resolving the system {(ground-speed and track),(wind-speed and direction),(airspeed and heading)}
The other side is a circular slide rule, also still very much in use.
the trajectory of the bullet following the exit of the rear of the plane will acquire a slight parabolic trajectory downwards in the direction of the plane’s path.
With gravity as a given, the bullet will attain an intial horizontal velocity wrt the ground as a result of air resistance from the draft of the plane.
Just as a regularly fired horizontal bullet has a parabolic trajectory due to a initial horizontal velocity and vertical force of gravity.
Sorry, but it doesn’t matter if it’s on a treadmill. Make it funny, but make it right.
I still don’t fly without one with me. I like new tech but… No batteries to go dead… So it is in my flight bag…
But that’s exactly what actually happens! (Ignoring factors others have mentioned such as air resistance.) Also for this answer, I interpret your phrase “fall immediately to the ground” to mean “fall straight down to the ground.”
Here’s a good video of Japanese experiment showing that physics principle. They fire a ball out the back of a moving truck. They calibrated the speed of the truck to match the speed of the gun so that the ball’s speed relative to the ground is 0 mph. You’ll clearly see the ball fall straight down to the ground.
(The background music is a little annoying and overdramatic but the payoff in physics knowledge at the end is worth it.)
I think you can substitute the truck for your cargo plane and the ball for your bullet and it will match the premise of your question.
Good find! Most relevant post!
That video is a classic. I love the way the driver is wearing a fire proof suit, racing gloves and a full face helmet to drive at, wait for it 100 km/hr! Great Og, that’s about 60mph! I hope he was a trained stunt driver. The risks people are prepared to take for science never cease to amaze me.
Great video, though.
Whereas the guy clinging on in the back operating dodgy spinning machinery gets nothing.
Cool. So if you had the 100 km/h ball launcher on the back of your truck going 100 km/h and wanted to shoot at pedestrians and road signs you wouldn’t damage either one.
To the person firing the gun, as well as everyone else on the plane, it would appear as a bullet moving 500mph away from a stationary gun. The bullet would seem to move away in a downward arc away from the plane.
To an observer on the ground, it would look like a gun moving at 500mph away from a stationary bullet. The bullet would seem to drop downward in a straight line.
In reality there might be minor lateral wind-resistance effects, but those are secondary to your question about frames of reference.
You laugh, but on many roads in Japan, 60mph in a 35mph zone can get you a $1000 fine and a license suspension for reckless driving. It’s a nation of Sunday drivers.
Nm.
Not exactly the same, as wind resistance inside the plane will slow the bullet down to 499.x mph before it exits the back of the plane. This leaves a slight positive forward velocity (500-499.x = 0.x mph, relative to ground) as it shoots out the rear.
I think it is interesting to imagine that if the truck were being chased by another car at 100kph, an observer in the car or truck would see the guy with the ball gun shooting at the other car just as if they were not moving. But an observer on the ground would see the first truck ‘dropping’ balls out the back which are then being ‘run into’ by the second car.
You know full well that we are talking about the simplified scenario and ignoring air resistance. The OP is interested in the basic analysis, not in all the minute complicating factors which include the humidity in the atmosphere, the coriolis force and the heartburn of the pilot.
I didn’t mean to come across as snarky, I was just including the information in case the OP is interested.
It will probably slow it a lot more than that. A 747 is around 75 yards long. Various Googling (c.f. this page - scroll down) suggests a bullet typically loses something like 20% of its velocity in this distance.
This will be affected by such things as the bullet’s ballistic coefficient and the density of the air. (But note that the need for the door to be open suggests that the altitude will not be especially high.)
One reason it’s hard to believe that a bullet fired out of a gun hits the ground at the same time as a dropped bullet is that guns are hardly ever fired exactly level. A small down tilt of the muzzle means the bullet hits the ground much faster than the dropped bullet, a small uptilt means it hits much later. You’d have to calibrate your gun pretty carefully to make sure it fires exactly parallel to verify that a fired bullet and a dropped bullet hit the ground at the same time. But anyone who does any shooting knows that bullets drop during flight and you have to compensate for that drop or you won’t hit your target. Bullets don’t travel in straight lines, they travel in parabolas.