### Video Transcript

How many times larger is the kinetic energy of a bullet of mass 0.005 kilograms that has a velocity of 500 meters per second and the kinetic energy of a drone with a mass of five kilograms and a velocity of five meters per second?

In this question, we’re studying two different objects. We’ve got a bullet. And we’ve got a drone. The bullet has a mass of 0.005 kilograms and a velocity of 500 meters per second. The drone, on the other hand, has a mass of five kilograms and a velocity of five meters per second.

We need to compare their two kinetic energies. In other words, we need to find out how many times larger the kinetic energy of the bullet is compared to the kinetic energy of the drone. So a sensible way of going about this is to first find the kinetic energy of the bullet. We’ll call this 𝐸 sub 𝑘 comma 𝑏. This is because it’s an energy 𝐸. And the subscripts tell us that it’s a kinetic energy 𝑘. And it’s the kinetic energy of the bullet 𝑏.

So this is the first thing we find out. Then we can find out 𝐸 sub 𝑘 comma 𝑑. That’s the kinetic energy of the drone. Finally, we need to find out how many times larger the kinetic energy of the bullet is compared to the kinetic energy of the drone.

So we can say that 𝐸 sub 𝑘 comma 𝑏, the kinetic energy of the bullet, is 𝑥 times 𝐸 sub 𝑘 comma 𝑑, the kinetic energy of the drone. And we’re trying to find out what the value of 𝑥 is. We can rearrange this equation to give us 𝐸 sub 𝑘 comma 𝑏 divided by 𝐸 sub 𝑘 comma 𝑑 is equal to 𝑥. And that will give us our final answer.

So let’s start by finding 𝐸 sub 𝑘 comma 𝑏. We can start by recalling the formula for the kinetic energy of an object. The kinetic energy 𝐸 sub 𝑘 is given by half multiplied by the mass of the object 𝑚 multiplied by the velocity of the object 𝑣 squared.

This is an important formula to remember. The kinetic energy of the object is half 𝑚𝑣 squared. So let’s use it to find 𝐸 sub 𝑘 comma 𝑏. This happens to be half multiplied by the mass of the bullet, 0.005 kilograms, multiplied by the velocity of the bullet, 500 meters per second, all squared.

Evaluating this gives us 625 joules. So we can place a nice little orange box around it and move on to 𝐸 sub 𝑘 comma 𝑑. This time, we have to use the mass and the velocity values given to us for the drone, not for the bullet. And this ends up being half multiplied by the mass of the drone, which is five kilograms, multiplied by the velocity of the drone, five meters per second, all squared.

Evaluating this expression gives us 62.5 joules, which means that it’s time for yet another cute little orange box. Finally, we know that we need to find the ratio 𝐸 sub 𝑘 comma 𝑏 over 𝐸 sub 𝑘 comma 𝑑. And this simply ends up being 625 divided by 62.5.

Simplifying the fraction gives us a value of 10. And, hence, our final answer is that 𝐸 sub 𝑘 comma 𝑏, the kinetic energy of the bullet, is 10 times larger than 𝐸 sub 𝑘 comma 𝑑, the kinetic energy of the drone.