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 want to find. We know that the rocket is burning fuel at a constant rate of 80 kilograms per
second. In other words, assuming that 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 every second. We also know that the initial mass of the rocket is 26 metric tons. We can then recall that one metric ton is equal to 1,000 kilograms. Therefore, the initial mass of the rocket must be 26,000 kilograms.
To find the total mass of the rocket 25 seconds after takeoff, we can find the total
mass of fuel lost in this time. We know that the rocket burns 80 kilograms of fuel every second. So, over a time period of 25 seconds, the rocket will have burned 80 times 25
kilograms of fuel, which we can calculate is 2,000 kilograms. The mass of the rocket after 25 seconds is then going to be equal to the initial mass
of the rocket minus the mass of the fuel burned by the rocket in the 25 seconds. That’s 26,000 kilograms minus 2,000 kilograms, which we can calculate is equal to
24,000 kilograms. Then, since the initial mass of the rocket is given in metric tons, we can convert
this to obtain 24 metric tons.
Hence, the mass of the rocket after 25 seconds is 24 metric tons.
