**When physicists stepped in, the mystery was solved.**

You won’t be able to count the number of falls from a window or balcony in a cat’s lifetime. For us humans, sometimes it’s just: 1. The fact that cats can miraculously survive falls from unbelievable heights.

A cat fell from a window on the 32nd floor of a building onto a New York street with only a broken rib and collapsed lung. For cats, this injury equates to just two days in the hospital before being able to go home.

But in the end, what helped the cats survive the fall from that height?

**When the cats do the math**

In a study conducted by the Journal of the American Veterinary Medical Association, scientists accounted for 132 events in which cats fell from buildings ranging from two stories to 32 feet tall. floor.

Statistics show that their average survival rate is 67%. But the number will go up to 90% if the cats are treated promptly and taken to the veterinary clinic. Confusingly, the height of the fall was not always proportional to the cats’ chances of survival.

From the 2nd to the 7th floor, the more you fall from a great height, the more seriously the cats are injured. But the scientists found that from a height of seven stories or more, the cats’ injuries seemed to level off. They couldn’t be more seriously injured when falling from the 32nd floor than from the 8th.

And only when physics comes in will the mystery be solved.

When a cat falls, there are essentially two forces acting on it. The downward gravitational force depends on the acceleration due to gravity (9.8 N/kg on Earth) and the mass of the cat. The other force is air resistance.

Air resistance increases with the speed of the cat during the fall and always pushes in the opposite direction of its motion. If the cat were to just fall vertically downwards, the equation for the sum of the y-direction forces acting on it would be:

For air resistance, ρ is the density of the air, A is the cross-sectional area of the cat, and C is the shape-dependent drag coefficient.

You can see that when the cat starts to fall, the velocity will be zero making the total force acting on the cat to be -m*g (like a free falling object). At this point, the cat will feel gravity pulling it down.

The force of the impact makes the cat know it is falling. And instinctively like when faced with a threat, the cat will arch its back, ruffle its fur and straighten its legs to get ready to land.

Foot landing is a great option when the cat falls from a relatively low height. But it would be a bad idea if their drop distance was longer. Cats can break all four legs and that limits their ability to survive because they can’t move to safety after a fall or try to find food.

So when falling from a greater height, the cats opted for a different strategy. They spread their limbs like a flying squirrel and land on their bellies.

But how do cats sense when they should land on their bellies? Let’s go back to the force equation. Ignoring the constants ρ, A and C, we see that as the velocity v increases, to a certain threshold, the air resistance will cancel out gravity. Then the total force acting on the cat will be zero. We call that the terminal velocity.

The scientists ran mathematical models to calculate the final speed a cat can reach during their fall to be about 97 km/h. And the distance to reach this speed is 18-21m, equivalent to 6-7 floors.

The final velocity will cause the cat to perceive the total force acting on it as zero. And at this point, it switches to the grounding strategy from paw to belly. The fact that cats spread their limbs, relax and land with large cross-sectional software ultimately reduces the force exerted on them.

Oftentimes, cats only end up injured and mostly survive the fall, especially when it comes to resuscitation. In fact, there have also been cats that fell from a height of 26 floors and got up right away and left the house.

**Don’t let your cat out of the window**

I really want to tag 18+ for this article, because if you are not mature enough, you will probably immediately find a cat to do experiments. In fact, cats’ instinct to “fly” doesn’t always help them survive a fall.

Cats have evolved to have sharp claws that help them climb and grip surfaces like wood and trees. But that was before man invented brick and mortar. A cat can slip and fall from an apartment window, because it forgets what material is under its feet.

Cats tend to be super focused on anything that interests them. A bird or bug flying right outside the window can agitate them with their feet and then be startled by loud noises or strong winds and fall.

The brick and mortar surface basically does not support the cat’s ability to grip. And the concrete underneath can kill it if not grounded properly. Do you still remember the ratio? One-third of cats will die without first aid and 10% even if they are taken to the vet.

So the advice is never to let a cat out of your window just to see how it lands. In addition, if you are living in a high-rise apartment building, you can buy window screens to protect your pets. If not, close the window so your cat is always safe.