Problem with Escape Velocity given final speed

In summary, the radius of Mercury is 2440 km and its mass is 0.31024 kg. An object is launched from just above the atmosphere of Mercury and needs an initial speed of sqrt{2GM- vfinal^2}=vinitial to reach a final speed of 2500 m/s when it is far from Mercury. However, the given mass may be incorrect and the formula provided by the poster is wrong dimensionally. It is suggested to carefully check the initial equation and redo the calculations step by step.
  • #1
celestasia
11
0

Homework Statement


The radius of Mercury (from the center to just above the atmosphere) is 2440 km (2440103 m), and its mass is 0.31024 kg. An object is launched straight up from just above the atmosphere of Mercury.
(a) What initial speed is needed so that when the object is far from Mercury its final speed is 2500 m/s?
vescape =

Homework Equations


1/2mvfinal^2-GMm/rfinal=1/2mvinitial^2-GMm/rfinal

The Attempt at a Solution



I tried to manipulate the formula algebraically. I got something like sqrt{2GM- vfinal^2}=vinitial. It's not working out. I think it has something to do with my algebra.
 
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  • #2
The mass of Mercury, as given, is ridiculously small.

The formula you have obtained is wrong dimensionally. Where is the radius of the planet in it? Perhaps you could just show the entire manipulation that gets you there.
 
  • #3
voko said:
The mass of Mercury, as given, is ridiculously small.

Since the poster apparently is not aware of how to format text on this forum I assume the given mass is to be read as 0.3∙1024 kg, which fits actual data.

I would suggest that the poster carefully checks the initial equation (which, apart from distracting formatting issues, also contains an error) and redo his calculations step by step. If the answer still mysteriously comes out wrong then by all means post the steps here for a hint or two.
 

FAQ: Problem with Escape Velocity given final speed

1. What is escape velocity?

Escape velocity is the minimum velocity required for an object to overcome the gravitational pull of a massive body, such as a planet or star, and escape its gravitational field.

2. How is escape velocity calculated?

The formula for calculating escape velocity is V = √(2GM/R), where V is the escape velocity, G is the gravitational constant, M is the mass of the massive body, and R is the distance between the object and the center of the massive body.

3. What is the problem with escape velocity given final speed?

The problem with escape velocity given final speed is that it does not take into account the direction of the object's velocity. In order to escape the gravitational pull of a massive body, the object must have a velocity that is both greater than the escape velocity and directed away from the body.

4. Can an object have a final speed greater than escape velocity and still not escape a planet's gravitational pull?

Yes, an object can have a final speed greater than escape velocity but still not escape a planet's gravitational pull if its velocity is not directed away from the planet. In order to escape, the object's velocity must be directed away from the planet.

5. How does escape velocity vary on different planets?

Escape velocity varies on different planets based on their mass and size. Generally, the larger and more massive the planet, the higher its escape velocity will be. For example, Earth's escape velocity is approximately 11.2 km/s, while the escape velocity on Mars is only 5 km/s due to its smaller size and mass.

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