 Look at this flea jumping through the air. With a lot of effort and some luck, the flea could land on one of its target and the whole itching cycle begins. How can the flea jump like this? And what is the velocity with which a flea should jump so that it reaches the height that it does? And finally, what is the height that humans would reach if they could jump like a flea? Let's try to answer all of those questions in this video. So here we have the flea, all ready to jump. And usually fleas they weigh around 0.5 milligrams and their height is 2 millimeters. On an average, a flea could reach a height of 30 centimeters when they jump. So let's say that a flea is jumping from the ground, here is a flea, and it jumps and reaches this height which we say is usually 30 centimeters. This is, and let me write this in meters, this is 0.3 meters. Now when the flea jumps, there will be some take-off velocity, right? There will be some take-off velocity, we can call this speed. And at the highest point, we can say that there is some velocity, but it has reached a height, so it has gained some gravitational potential energy. All of this initial kinetic energy has changed to gravitational potential energy. And we can apply the conservation of energy principle. We can try and figure out the take-off velocity from that. We are not considering any form of air resistance. So we can write half mv square, that is the initial kinetic energy, equals to the gravitational potential energy, and there is no kinetic energy at the highest point. So this is equal to mgh. The good thing about this is that mass gets cancelled off. So m, we don't have to deal with m, v square is equal to 2gh. So v, this is equal to under root of 2gh. And when we work this out, when we plug in values, g and h, g we can take as 10, h is 0.3. So this is really under root of 2 into 10 into 0.3. And this is, this is 6. So under root of 6 is approximately 2.5, 2.45, 2.45 meters per second. So these are the take-off velocities for fleas mostly. Now despite not seeing much, but let's try to understand this from the perspective of a flea. So a flea is only 2 millimeters tall, and it can reach a height of 30 centimeters. How would that look like in human terms? Let's say the height of some human, that's, it's 2 meters, let's say it is 2 meters. Now if a flea being 2 millimeters can jump a height of 30 centimeters, a human who is 2 meters tall, what would the height look like for a 2 meter, 2 meter tall human who could jump like a flea? So let's try and work that out. If this is, we are considering the ratios to be the same. So we are considering the, how tall the flea is, that is 2 millimeters. This is divided by 30 centimeters, and, and a human, human's height, we are considering this as 2 meters divided by the height that we want to figure out if a human could jump like a flea. Now these are in different units. This is centimeters, this is millimeters, this is meters. We need to change, let's keep all of them in meters. This is 2 into 10 to the power minus 3 divided by 30 into 10 to the power minus 2. This is equal to 2 divided by h. Now many things get canceled off and when we work this out, the height, this height comes out to be equal to 300 meters. So this really means that if a human could jump like a flea, they would be able to reach a height of 300 meters to put it in perspective. That means in a, in a single jump, you are able to reach the top of this building from the ground. And if we try and understand the velocity with which a human should jump to be able to reach that height, we can again apply conservation of energy principle. We can, we can write, let's, let's remove this again. We can, we can write half mv square that is equal to mgh. So that's really, that's really half into mv square equals to mgh. Again m gets canceled off and v is under root of 2gh, but h here is 300 meters. So this is 2 into 10 into 300. So this is 20 into 300 under root of 6,000. And this, this is 77.4 meters per second. This is just incredibly high. Now the big question is how can a flea jump like that? What does a flea possess? What does a flea have that it can jump? It can make that incredible jumps. So, so it, it comes to a kind of protein which is called resilent. Let me, let me remove this, let me remove this all together. It's a kind of protein which is called, which is called resilent. And this protein makes the muscles very elastic, kind of like how a spring would act. So if you have a spring and if you have a ball on top of a spring, when you compress it, when you compress it like this, and then when you let it go, the ball would reach incredible heights, kind of like this, the ball lifts off and reaches great height. Similarly, how a flea's legs act when, when a flea compresses its legs. Because of resilent, the muscles act like springs. They store all of this, all of this elastic energy. And when the flea takes off, when it lifts off, it kind of extends like a spring, giving the flea some incredible speed so that it can reach a great height. And unfortunately, we don't have that. So we are nowhere close to how a flea could make a jump.