Final speed of an asteroid using escape speed

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Homework Help Overview

The problem involves calculating the final speed of a rock thrown from a small asteroid, given its escape speed and the initial speed of the rock. The subject area pertains to gravitational physics and energy conservation principles.

Discussion Character

  • Exploratory, Conceptual clarification, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss various interpretations of how to calculate the final speed, with some suggesting simple subtraction of escape speed from the initial speed, while others propose using energy conservation principles to derive the final speed.

Discussion Status

The discussion is active, with participants offering different methods and seeking clarification on the reasoning behind the calculations. There is an acknowledgment of the need for understanding the underlying concepts rather than just arriving at an answer.

Contextual Notes

Some participants note the lack of specific values for mass and radius, which may affect the calculations. The original poster expresses uncertainty about how to approach the problem given these constraints.

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Homework Statement



The escape speed from a very small asteroid is only 32 m/s. If you throw a rock away from the asteroid at a speed of 44 m/s, what will be its final speed?

Homework Equations



Ki + Ui = 1/2mv^2 + (-GMm/R) = 0 (for v<<c)

The Attempt at a Solution



I am unsure of how to do this problem because I don't have the masses or the radius. Any help would be greatly appreciated!
 
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Isn't it just 44 - 32?
 
It should be SQRT((44^2)-(32^2))
 
Thank you! However, I would like to know the steps on how you got to the answer if possible...
 
The definition of escape speed is that it is the v that provides sufficient KE to take the object infinitely far away from the planet, where its velocity will then be zero.
So your object will have E = 1/2*m*44^2 - 1/2*m*32^2 energy leftover.
Put this back in E = 1/2*m*v^2 to see what the speed due to the leftover energy is.
No doubt guitarman has it right, but yes, you most definitely want to know why!

Thanks to guitarman for catching my mistake!
 

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