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An astronaut of mass 210 $\mathrm{kg}$ including his suit and jet pack wants to acquire a velocity of 2.0 $\mathrm{m} / \mathrm{s}$ to move back toward his space shuttle. Assuming the jet pack can eject gas with a velocity of $35 \mathrm{m} / \mathrm{s},$ what mass of gas will need to be ejected?
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Physics 101 Mechanics
Chapter 9
Linear Momentum
Motion Along a Straight Line
Kinetic Energy
Potential Energy
Energy Conservation
Moment, Impulse, and Collisions
Simon Fraser University
University of Winnipeg
McMaster University
Lectures
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In physics, the kinetic energy of an object is the energy which it possesses due to its motion. It is defined as the work needed to accelerate a body of a given mass from rest to its stated velocity. Having gained this energy during its acceleration, the body maintains this kinetic energy unless its speed changes. The same amount of work is done by the body in decelerating from its current speed to a state of rest. The kinetic energy of a rotating object is the sum of the kinetic energies of the object's parts.
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Okay, so does Chapter nine. Problem 1 11 So it's as Anne Ashman, out of a mass to 10 kilograms including a soup and jetpack, wants to require a velocity two years, percent it to move back towards space travel. Assuming the jet pack, can you just inject gas with Ava last year of 35 meters per second? What mass gas We need to be injected. Okay, but we know that we can take a use equation. 9 19 this equation. Cool. Then we can rearrange this now. It's so for our separate variables and see that you have TV over the relative velocity because tm over and since the relative velocity of gap the gas here, these are the same and that's a constant cannot integrate both sides. And we see that the final over the relative calls the natural log of final over initial mass. You can rewrite this as a queen is Ah, equation for mass were in final cool seat in the shoulder, times the exponential of the overview gas. Okay, so now we can figure out what the master of the objective is. Mass of the ejected is in minus and final or in missile. That was initial times in the file. More speed over G. Do this to your killer grandsons. One minus you. Final C was two meters per second over. The gas was 35 feet is exponential of that, we get roughly 12 kilograms. That's how much gas we need to sit down. Cool.
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