Final speed of an asteroid using escape speed

In summary, the conversation discusses the concept of escape speed and how it applies to a small asteroid. The problem is to calculate the final speed of a rock thrown away from the asteroid at a given initial speed. The formula for calculating escape speed is mentioned and there is a discussion about the necessary information needed to solve the problem. The correct solution is provided, along with an explanation of the steps involved in obtaining the answer.
  • #1
enchanteuse
10
0

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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  • #2
Isn't it just 44 - 32?
 
  • #3
It should be SQRT((44^2)-(32^2))
 
  • #4
Thank you! However, I would like to know the steps on how you got to the answer if possible...
 
  • #5
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!
 

What is escape speed?

Escape speed is the minimum speed that an object needs to travel in order to break free from the gravitational pull of another object. In the context of an asteroid, it is the speed needed to escape the gravitational pull of a planet or other celestial body.

How is escape speed calculated?

The formula for escape speed is sqrt(2GM/R), where G is the gravitational constant, M is the mass of the planet or celestial body, and R is the distance from the center of the planet to the object's starting point. This formula takes into account the gravitational force of the planet and the kinetic energy of the object.

What factors affect the final speed of an asteroid using escape speed?

The final speed of an asteroid using escape speed is affected by the mass and size of the planet or celestial body, as well as the distance between the planet and the asteroid. The escape speed will also vary depending on the starting point of the asteroid, as it may be closer or farther from the planet's center of gravity.

Can an asteroid's final speed exceed escape speed?

Yes, an asteroid's final speed can exceed escape speed if it is given an additional boost of energy. This can happen if the asteroid is propelled by a force, such as the gravitational pull of another object, or if it undergoes a collision or explosion.

Why is escape speed important in relation to asteroids?

Escape speed is important in relation to asteroids because it determines whether an asteroid will remain in orbit around a planet or if it will be thrown out into space. It also plays a role in the potential impact of an asteroid on a planet, as a higher escape speed means a greater force of impact.

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