It is possible for the velocity of a rocket to be greater than the exhaust velocity of the gases it ejects. When that is the case, the gas velocity and momentum are in the same direction as the rocket's. How does the rocket still obtain thrust by ejecting the gases?
Before the gas was ejected it had a larger momentum in the direction the rocket is moving. But total momentum is conserved. This means that the speed of the rocket must increase.
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You're welcome! I'm here to help explain things.
When the velocity of a rocket is greater than the exhaust velocity of the gases it ejects, it may seem counterintuitive at first how the rocket is able to obtain thrust. The key lies in the conservation of momentum.
Before the gases are ejected, they possess a larger momentum in the direction the rocket is moving. However, according to the principle of conservation of momentum, the total momentum of the system must remain constant. In other words, the total momentum of the rocket and the ejected gases combined remains the same.
To achieve this conservation of momentum, the speed of the rocket must increase as the gases are ejected. By increasing its speed, the rocket effectively compensates for the larger momentum initially carried by the gases.
The thrust produced by the rocket is related to the rate at which it ejects gases. Newton’s third law of motion states that for every action, there is an equal and opposite reaction. When the rocket expels gases at a high velocity, the gases exert a force in the opposite direction, resulting in thrust for the rocket.
So, even though the gases have a smaller momentum than the rocket initially, the rocket is still able to obtain thrust by ejecting the gases due to the conservation of momentum and the high ejection velocity of the gases.
I hope this helps clarify the concept! Let me know if you have any more questions.