Video: Finding the Final Value of a Quantity given Its Initial Value and Constant Rate of Change

Given that a rocket of mass 26 metric tons is burning fuel at a constant rate of 80 kg/s, find the mass of the rocket 25 seconds after takeoff?

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Video Transcript

Given that a rocket of mass 26 metric tons is burning fuel at a constant rate of 80 kilograms per second, find the mass of the rocket 25 seconds after takeoff?

Let’s begin by identifying what we know and what we’re trying to find. We know that the rocket is burning fuel at a rate of 80 kilograms per second. In other word, assuming the rocket isn’t losing mass from anywhere else, which is a safe assumption to make, we know that the rocket is losing 80 kilograms of its mass per second. We also know that the rocket initially, in other words, when 𝑡 is equal to zero, has a mass of 26 metric tons. One metric ton is equal to 1000 kilograms, so the starting mass of the rocket must be equal to 26000 kilograms.

To find the total mass of the rocket 25 seconds after takeoff, we can find the total amount of fuel lost in this time. We know it loses 80 kilograms per second. So, after 25 seconds, it will have lost 80 times 25 kilograms. That’s 2000 kilograms in 25 seconds. The new mass of the rocket after 25 seconds will, therefore, be 26000 minus 2000. That’s 24000 kilograms, which is 24 metric tons. And so, the mass of the rocket after 25 seconds is 24 metric tons.

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