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.