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(II) A rocket traveling 1850 $\mathrm{m} / \mathrm{s}$ away from the Earth at an altitude of 6400 $\mathrm{km}$ fires its rockets, which eject gas at a speed of 1300 $\mathrm{m} / \mathrm{s}$ (relative to the rocket). If the mass of the rocket at this moment is $25,000 \mathrm{kg}$ and an acceleration of 1.5 $\mathrm{m} / \mathrm{s}^{2}$ is desired, at what rate must the gases be ejected?

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$-76 k g / s$

Physics 101 Mechanics

Chapter 9

Linear Momentum

Motion Along a Straight Line

Kinetic Energy

Potential Energy

Energy Conservation

Moment, Impulse, and Collisions

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Okay, So chapter in our own problem. 83 year. So it says the rocket is traveling 18 50 meters per second away from earth. Altitude of 6400 kilometres fires its rockets which reject its speed. 1300 meters per second relative. A rocket If the mass of the rocket at this moment is so mass at T 0 2500 kilograms Acceleration 1.5 meters per second. Desire what rate must cast you. Okay, well, this is a lot of information, but we're gonna use Equation 1 19 point nine point late. Looking for Bea told us the mass times the acceleration here it's given by the external force plus the relative velocity the re of mass injected. Okay, so we can rearrange this or what the duty is. And this becomes one over a relative velocity times The total mass Dutt my is the extra horse. Okay, so this becomes one over the road to velocity tyres mass DVD T minus G in earth Mass of the rocket over r squared. Now we can put everything in so we have won over The relative speed is 1300 1300 This percentage Now we have the masses. 25 1000 grains DVD T 1.5 square meters is our acceleration. Now we have a big G. This guy 11 times the mass of the earth or kilograms times 25,000 kilograms all over. What was the altitude? It says the attitude was 6400 coop birds. So we had to take the radius of the earth, uh, 6.4 kilometers Union square. Awesome. So there's a lot of stuff here, but we can just plug it all calculator. Sorry for the sloppiness here, but it comes out being negatives. 76 kilograms per second is the rate of change of mass, which means we're ejecting mass ass seventies, six kilograms per second. It was positive we would be absorbing mass, but that's not what rockets do.

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