explain rocket propulsion in terms of momentum conservation

Another common example is the recoil of a gun. Explain rocket propulsion in terms of momentum conservation. By conservation of momentum, the rocket’s momentum changes by this same amount (with the opposite sign). Conservation of energy demands [latex]\frac{1}{2}{m}_{1}{v}_{\text{1,i}}^{2}+\frac{1}{2}{m}_{2}{v}_{\text{2,i}}^{2}=\frac{1}{2}{m}_{1}{v}_{\text{1,f}}^{2}+\frac{1}{2}{m}_{2}{v}_{\text{2,f}}^{2}[/latex]. This work is licensed by OpenStax University Physics under a [ "article:topic", "authorname:openstax", "rocket equation", "license:ccby", "showtoc:no" ][ "article:topic", "authorname:openstax", "rocket equation", "license:ccby", "showtoc:no" ]
Now we deal with the case where the mass of an object is changing. The space shuttles required seven pounds of fuel for every pound of payload they carry. (d) Which premise is unreasonable, or which premises are inconsistent?Two 70-kg canoers paddle in a single, 50-kg canoe. In other words, spacecrafts eject mass in a certain direction in order to be propelled in another. In part (b), a time Δt has elapsed in which the rocket has ejected a mass Δm of hot gas at a velocity vBy calculating the change in momentum for the entire system over Δt, and equating this change to the impulse, the following expression can be shown to be a good approximation for the acceleration of the rocket. [latex]{v}_{\text{1,f}}={v}_{\text{1,i}}\frac{{m}_{1}-{m}_{2}}{{m}_{1}+{m}_{2}},\,{v}_{\text{2,f}}={v}_{\text{1,i}}\frac{2{m}_{1}}{{m}_{1}+{m}_{2}}[/latex]Repeat the preceding problem for the case when the initial speed of the second object is nonzero.A child sleds down a hill and collides at 5.6 m/s into a stationary sled that is identical to his. Thus, the initial momentum of the system is \(\vec{p}_{i}\) = mv \(\hat{i}\).The rocket’s engines are burning fuel at a constant rate and ejecting the exhaust gases in the −x-direction.
[latex]\text{−}(24\times {10}^{3}\,\text{N})\mathbf{\hat{i}}[/latex]Two hockey players approach each other head on, each traveling at the same speed [latex]{v}_{\text{i}}[/latex]. Ex 6.26 In Chapter 5, rocket propulsion was explained in terms of Newton's third law. propellant ratio of the ”rocket” is 50%. Their paddling moves the canoe at 1.2 m/s with respect to the water, and the river they’re in flows at 4 m/s with respect to the land. Combining these equations with the equation given by conservation of momentum gives [latex]{v}_{\text{1,i}}={v}_{\text{1,i}}[/latex], which is true, so conservation of momentum is satisfied. Just before launching, the momentum of the rocket is zero.

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