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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?
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In this question, weβre studying two different objects.
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Weβve got a bullet.
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And weβve got a drone.
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The bullet has a mass of 0.005 kilograms and a velocity of 500 meters per second.
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The drone, on the other hand, has a mass of five kilograms and a velocity of five meters per second.
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We need to compare their two kinetic energies.
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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.
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So a sensible way of going about this is to first find the kinetic energy of the bullet.
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Weβll call this πΈ sub π comma π.
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This is because itβs an energy πΈ.
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And the subscripts tell us that itβs a kinetic energy π.
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And itβs the kinetic energy of the bullet π.
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So this is the first thing we find out.
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Then we can find out πΈ sub π comma π.
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Thatβs the kinetic energy of the drone.
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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.
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So we can say that πΈ sub π comma π, the kinetic energy of the bullet, is π₯ times πΈ sub π comma π, the kinetic energy of the drone.
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And weβre trying to find out what the value of π₯ is.
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We can rearrange this equation to give us πΈ sub π comma π divided by πΈ sub π comma π is equal to π₯.
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And that will give us our final answer.
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So letβs start by finding πΈ sub π comma π.
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We can start by recalling the formula for the kinetic energy of an object.
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The kinetic energy πΈ sub π is given by half multiplied by the mass of the object π multiplied by the velocity of the object π£ squared.
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This is an important formula to remember.
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The kinetic energy of the object is half ππ£ squared.
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So letβs use it to find πΈ sub π comma π.
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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.
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Evaluating this gives us 625 joules.
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So we can place a nice little orange box around it and move on to πΈ sub π comma π.
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This time, we have to use the mass and the velocity values given to us for the drone, not for the bullet.
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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.
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Evaluating this expression gives us 62.5 joules, which means that itβs time for yet another cute little orange box.
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Finally, we know that we need to find the ratio πΈ sub π comma π over πΈ sub π comma π.
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And this simply ends up being 625 divided by 62.5.
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Simplifying the fraction gives us a value of 10.
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And, hence, our final answer is that πΈ sub π comma π, the kinetic energy of the bullet, is 10 times larger than πΈ sub π comma π, the kinetic energy of the drone.