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A cat will sometimes fall out of a window or balcony, no doubt as a result of a cat doing cat things. If you have a house cat, you probably aren't concerned about his or her proclivity for aerial antics: Cats may utilize their righting reflex to land on their feet as if nothing occurred when they fall out of low windows. However, if they fall from a higher story—a condition known as high-rise syndrome—they may not be as fortunate.

But here's the strange part: cats can survive falls from very high floors. According to a RadioLab program on the falling cat problem, cats falling five to nine storeys are the most likely to be harmed. However, if you fall from a higher storey, your chances of surviving improve.

But how do you do it? How is it feasible for a cat to have a better chance of surviving if it falls from a higher height? Air resistance and perceived weight are two factors that influence the response.

When an item falls, it is subjected to two opposing forces. The gravitational downward force is determined by the gravitational field (9.8 N/kg on Earth) as well as the mass of the item. The air resistance force is the other force. Air resistance is a force that rises in proportion to the object's speed and always pulls in the opposite direction of the object's motion.

How it all went down in the video

During an apartment fire in Englewood, a cat leapt out a window and survived the fall, which was captured on camera.

At 65th and Lowe, Chicago firemen responded to a fire in one unit of a multistory apartment complex. According to fire authorities, firefighters were just trying to put out hot spots at the moment and prevent the fire from spreading or affecting additional apartments.

Smoke can be seen pouring from broken, open windows in one or two apartments on the fifth story, according to a video shared on Twitter by the Chicago Fire Department. Following that, a tiny black shadow emerges after a few minutes.

It's a black cat peering carefully through one of the shattered windows. It assesses the distance below, momentarily checks the building's side with its front paws, and then leaps.

As the cat falls, there is an audible gasp from spectators, but it effortlessly avoids the apartment building's wall and lands on all four feet with a bounce on the grass beyond it. Following that, the cat bolted.

There has been no word on what caused the fire or how much damage has been recorded. There were no injuries recorded.

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The science behind your cat's super powers

But how can you calculate a cat's velocity as it falls from a building? Because the net force varies as it descends, it's not a straightforward issue. Creating a numerical computation is the only method to determine the speed. The motion is split down into numerous tiny time increments using a numerical computation. The forces are roughly constant at each of these time steps, allowing the motion to be computed. The better the computation, the fewer the time steps. The more time steps you have, though, the more computations you'll require. The only practical method to accomplish this is to use a computer program.

I don't have all of the numbers, so I'll have to guess at some (such a cat's mass and area), but here's my numerical model for a cat falling from a really tall structure (100 meters). You can view and edit the code by clicking the "pencil" icon—don't worry, you won't screw it up. Oh, and for comparison's sake, I also included an item with no air resistance.

The red curve (the item with no air resistance) has a parabolic shape, which is what you'd anticipate for continuous acceleration. However, due of the increased air resistance, the cat's speed does not increase with time.

This graph, however, fails to explain why intermediate falling distances are riskier than higher falling distances. How about a graph showing the falling cat's impact speed vs. its beginning height? You may look at the code and modify it if you like by clicking the "pencil" once again.

The basic consequence of a higher fall is a faster impact speed, as seen in this graph. As a result, air resistance alone cannot account for why a medium fall is riskier than a high fall.

Something else has to be considered. What about the perceived weight? The gravitational pull is not the same magnitude as your perceived weight. The amount of the force pushing against the gravitational pull is what matters. Consider the following scenario: you are in a motionless elevator and you press the down button. The elevator speeds downhill for a short time, and you feel a little lighter. Of course, your weight remained the same; the amount of the force exerted by the floor on you dropped. This is the weight you seem to be.

There is no air resistance force and nothing pushing up against the gravitational force when a cat first leaps (or falls) from a lofty window. The cat will feel weightless for a brief amount of time. The cat's instincts kick in during this weightlessness phase.

There is an evolutionary trick involve

A cat's survival may be contingent on two factors. First, there's the impact velocity. Higher impact speeds are undesirable because the cat will strike the ground more quickly. The perceived weight upon impact is the second factor to consider. Lower seeming weights are undesirable because the cat will be forced to land on its feet rather than stretched out and comfortable. I created an arbitrary survival score by adding the impact velocity (multiplied by some factor) and the inverse of the impact acceleration (multiplied by some factor). So you have two competing variables, but their connections to the beginning height are diametrically opposed. This implies that there should be a certain height that reduces this survival. This is a graph showing the score for various dropping heights.