Calculating the Speed of Exhaust Gas for a Rocket in Deep Space

In summary, in deep space where gravity is negligible, a rocket ejects 1/160 of its mass as exhaust gas in the first second and has an acceleration of 15.9 m/s2. The question is asking for the velocity of the exhaust gas relative to the rocket, expressed numerically in kilometers per second. Using the conservation of momentum equation, the problem can be solved by setting the change in momentum of the rocket equal to the change in momentum of the exhaust gas. This can be further simplified to find the velocity of the exhaust gas. However, since a value for the mass of the rocket is not given, a different equation (F = m*a) can be used to solve for the velocity.
  • #1
ch010308
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Homework Statement



A rocket is fired in deep space, where gravity is negligible. In the first second it ejects 1/160 of its mass as exhaust gas and has an acceleration of 15.9 m/s2.

What is the speed vgas of the exhaust gas relative to the rocket?
Express your answer numerically in kilometers per second.

Homework Equations



conservation of momentum: (m1v1 + m2v2)final = (m1v1 + m2v2)initial

The Attempt at a Solution



(159/160)M(vrocket + 15.9) - (1/160)Mvgas = Mvrocket

I go on to simplify it but I can't express vgas in numerical terms, as vrocket still remains in the equation. There is no value given for this so how can I solve the question?

Pls help! Thanks! :)
 
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  • #2
What's wrong with F = m*a = Δmv/Δt ?
 
  • #3
hmmm... Are you saying that i should use m*a = Δmv/Δt for the change in momentum of the rocket? then wat will be the value of m? :confused:
 
  • #4
ooohh! I got it now! Thanks for the help! :)
 

Related to Calculating the Speed of Exhaust Gas for a Rocket in Deep Space

1. How does a rocket travel in deep space?

A rocket travels in deep space by using a combination of its engines and the gravitational pull of planets and other celestial bodies. The rocket's engines provide the initial thrust needed to escape Earth's orbit, and then the gravitational pull of other objects helps to propel the rocket further into space.

2. How long does it take for a rocket to reach deep space?

The amount of time it takes for a rocket to reach deep space depends on several factors, such as the size and speed of the rocket, the distance to the destination, and the route taken. Generally, it can take anywhere from a few months to several years for a rocket to reach deep space.

3. What is the purpose of sending a rocket into deep space?

The purpose of sending a rocket into deep space is for exploration and scientific research. By sending rockets with advanced equipment and technology, scientists can gather data and images from distant planets, stars, and galaxies, helping us to better understand the universe and our place in it.

4. How do scientists communicate with a rocket in deep space?

Scientists communicate with a rocket in deep space using radio waves. The rocket is equipped with a receiver and transmitter that can send and receive signals from Earth. These signals are then decoded and analyzed by scientists to monitor the rocket's status and make any necessary adjustments.

5. What are the challenges of sending a rocket into deep space?

Sending a rocket into deep space poses several challenges, including the long distance and time it takes to reach the destination, the harsh environment of outer space, and the need for precise calculations and adjustments to ensure the rocket's success. Additionally, the cost and resources required for such a mission can be significant.

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