The most dangerous moment for our travelers would represent those few hundredths of a second, during which the cabin-projectile moves in the channel of the gun. Because during this negligible amount of time the speed with which passengers will move in a gun, should increase from zero to 16 km/sec! No wonder the novel passengers with awe waited for the shot. And Barbicane was quite right in asserting that the moment when the projectile will fly, will be for passengers as dangerous as if they were not inside, and in front of the projectile. Indeed, at the moment of shooting the lower Playground cabins will hit passengers from below with the same force with which would have hit the projectile to every body, being on its way. The novel's characters react to this danger too easy, imagining that get off in the worst case, only a rush of blood to the head...
The situation is more serious. In the barrel, the projectile is moving rapidly: the rate at which it grows under the constant pressure of the gases formed in the explosion. Within a tiny fraction of a second to rate this increases from 0 to 16 km/s. Let us assume for simplicity that the increased speed is performed uniformly, then the acceleration is necessary to ensure that in such a small time to bring the speed up to 16 km/s to reach here round score of 600 km per second per second (calculations shown next).
Fatal this figure we shall quite understand if you remember that the normal acceleration of gravity on the earth's surface is equal to just 10 meters per second per second*. It follows that every object inside the projectile at the moment of shot would be at the bottom of the cabin pressure, which is 60,000 times more weight this subject. In other words, passengers would feel that he had become like a few tens of thousands of times heavier! Under the action of such enormous gravity, they would be instantly crushed. One cylinder of Mr. Barbicane be weighed at the time of the shot not less than 15 tons (the weight of the loaded car); this hat is more than enough to crush its owner.
However, the novel describes the measures taken to mitigate impact: the core with a spring buffers and double bottom with water, filling the space in it. Duration of impact from this little stretched, and therefore, fast slew rate weakens. But when great forces with which we have here to deal, benefit from these devices get miserable. The force that will keep passengers to the floor, reduced to a tiny fraction, but does it matter to be crushed hat in 15 or 14 tons?!
* Will add that the acceleration of a racing car, his novice fast movement, does not exceed 2-3 m per second per second, and acceleration of the train, smoothly extending from station - 1 m per second per second.