Rocket Propulsion Homework: Calculating Travel Time

In summary: Please try to be more careful about what you post.In summary, a rocket with a payload of 4050.0 kg and 1.753·105 kg of fuel expels propellant at a speed of 4.300 km/s. It starts from rest, accelerates to its final velocity, and then begins its trip. The time it takes for the rocket to travel a distance of 3.82 ·105 km can be found using the equation Vc = ln(mi/mf). However, the values for rp and Tmax are needed, which are not provided in the given information.
  • #1
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Homework Statement


A rocket in outer space has a payload of 4050.0 kg and 1.753·105 kg of fuel. The rocket can expel propellant at a speed of 4.300 km/s. Assume that the rocket starts from rest, accelerates to its final velocity, and then begins its trip. How long will it take the rocket to travel a distance of 3.82 ·105 km


Homework Equations


[itex] V [sub c] ln(m [sub i]/ m [sub f])


The Attempt at a Solution

 
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  • #2
I found the final velocity, but when i tried to use the formula for distance, I found that I didn't have r sub p or T max and have no clue how to find them.
 
  • #3
You need to post all the equations you are referring to and define any symbols in them which might not be completely obvious to readers. (Even the "relevant equation" you posted is not an equation.)
 
  • #4
Psyguy22 said:

Homework Statement


A rocket in outer space has a payload of 4050.0 kg and 1.753·105 kg of fuel. The rocket can expel propellant at a speed of 4.300 km/s. Assume that the rocket starts from rest, accelerates to its final velocity, and then begins its trip. How long will it take the rocket to travel a distance of 3.82 ·105 km
Psyguy22, please look at what you posted. You did not mean 1.753·105 kg of fuel, you meant 1.753·105 kg of fuel. There's a huge difference between 184.065 kilograms and 17,530 kilograms.
 
  • #5

To calculate the travel time of the rocket, we first need to determine the final velocity of the rocket using the rocket equation:

[itex] V [sub f] = V [sub e] ln(m [sub i]/ m [sub f])

Where V [sub e] is the exhaust velocity (4.300 km/s), m [sub i] is the initial mass (4050.0 kg + 1.753·105 kg), and m [sub f] is the final mass (4050.0 kg).

Plugging in the values, we get:

[itex] V [sub f] = 4.300 km/s ln(1.753·105 kg/ 1.791·105 kg)

Solving for V [sub f], we get:

V [sub f] = 4.300 km/s ln(0.9778)

V [sub f] = 4.300 km/s (-0.0222)

V [sub f] = -0.095 km/s

Now, we can use the equation:

[itex] t = d/V [sub f]

Where t is the travel time, d is the distance (3.82·105 km), and V [sub f] is the final velocity we just calculated.

Plugging in the values, we get:

t = 3.82·105 km/ (-0.095 km/s)

t = -4.02·106 s

Therefore, it will take approximately 4.02 million seconds for the rocket to travel a distance of 3.82·105 km.
 

What is rocket propulsion and how does it work?

Rocket propulsion is a method of creating thrust or forward motion by ejecting hot, high-speed gas from the back of a rocket. This gas is created by burning a fuel and an oxidizer in a combustion chamber. The hot gas is then directed through a nozzle, which accelerates it and creates a reaction force that propels the rocket forward.

What factors affect the travel time of a rocket?

The travel time of a rocket is affected by several factors, including the amount of thrust generated by the rocket engine, the weight of the rocket, the distance it needs to travel, and the efficiency of the rocket's design. Other factors such as external forces like gravity and air resistance may also play a role in the travel time.

How do you calculate the travel time of a rocket?

The travel time of a rocket can be calculated using the rocket equation, which takes into account the mass of the rocket, the mass of the propellant, and the exhaust velocity of the rocket engine. Other variables like the distance to be traveled and external forces can also be factored in to get a more accurate calculation.

What is the importance of calculating travel time for rocket propulsion?

Calculating travel time for rocket propulsion is important for planning and executing space missions. It helps scientists and engineers determine the amount of fuel and propellant needed for a specific mission, as well as the optimal trajectory and course for the rocket to take. It also allows for more accurate predictions of when a rocket will reach its destination.

How does rocket propulsion differ from other forms of propulsion?

Rocket propulsion differs from other forms of propulsion in that it does not require any external medium, such as air or water, to create forward motion. This allows rockets to travel through the vacuum of space. It also produces much higher velocities than other forms of propulsion, making it ideal for long-distance space travel.

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