Speed of a Rocket far from Earth

In summary, a rocket with a launch speed of 1.60×10^4 m/s is launched straight up from the Earth's surface. To find its speed when it is very far away from the Earth, we can use the equations F= (GMm)/r^2, G= 6.67 X 10^-11, M= 5.98 X 10^24, Potential Energy = (Gm1m2)/r, Kinetic Energy = 1/2mv^2, and Escape velocity= 11200 m/s. Initial attempts to solve the problem by subtracting the launch speed from the escape velocity were incorrect. The correct approach is to use conservation of energy, setting up the
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Homework Statement



A rocket is launched straight up from the Earth's surface at a speed of 1.60×10^4 m/s.
What is its speed when it is very far away from the earth?

Homework Equations


F= (GMm)/r^2
G= 6.67 X 10^-11
M= 5.98 X 10^24

Potential Energy = (Gm1m2)/r
Kinetic Energy = 1/2mv^2
Escape velocity= 11200 m/s

The Attempt at a Solution



My first attempt was to take the speed of the rocket (1.60 X 10^4) and subtract it from the escape velocity. This gave me 4800 m/s. This assignment is online and the program said that answer is incorrect. Now I am not sure how to approach the problem. Does anyone have advice as to how to start this problem? All help is greatly appreciated. Thank you.
 
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  • #2
Try using conservation of energy.
 
  • #3
Conservation of energy was my second attempt. I set it up as this:

P.E. + K.E. = K.E. + P.E.


OH! I see. Dang, for some odd reason the first time I tried this approach I used 9.8 as the value for P.E. ...how foolish. I see now. Thank you so much. Man, I cannot afford to do that on a test. Thanks again.
 

FAQ: Speed of a Rocket far from Earth

1. What is the speed of a rocket far from Earth?

The speed of a rocket far from Earth can vary greatly depending on its purpose and design. Some rockets, such as those used for space exploration, can reach speeds of over 25,000 miles per hour. Others, like those used for satellite launches, may reach speeds of around 17,000 miles per hour. The speed at which a rocket travels is also affected by the gravitational pull of other celestial bodies.

2. How is the speed of a rocket measured?

The speed of a rocket is typically measured in miles per hour (mph) or kilometers per hour (km/h). In some cases, it may also be measured in meters per second (m/s) or even kilometers per second (km/s). The speed can be calculated by dividing the distance traveled by the time it took to travel that distance.

3. Can a rocket travel faster than the speed of light?

No, according to Einstein's theory of relativity, nothing can travel faster than the speed of light. This means that rockets, no matter how advanced, cannot exceed the speed of light, which is approximately 670 million miles per hour.

4. How does the speed of a rocket affect its fuel consumption?

The speed of a rocket directly impacts its fuel consumption. As a rocket travels faster, it needs more fuel to maintain its speed and overcome the resistance of the air and other forces. This is why rockets are designed to be as efficient as possible, using the least amount of fuel to achieve their desired speed.

5. What factors can affect the speed of a rocket far from Earth?

The speed of a rocket far from Earth can be affected by various factors, including its size and weight, the amount of thrust it produces, the atmosphere and gravitational pull of other celestial bodies, and any external forces acting upon it. The design and technology of the rocket also play a crucial role in determining its speed.

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