Can Stone Escape an Asteroid's Gravitational Pull?

[imy786]

Homework Statement

Is it possible that you could throw a stone with sufficient energy to cause it to escape the asteroid’s gravitational pull altogether.

Do you think you would be able to throw the stone as fast as this?

Homework Equations

v= squre root of (2GM / R)

where M is mass of the Earth
and
R is the radius of the earth

The Attempt at a Solution

M= 5.98*10^24
R=6.38*10^6
G=6.67*10^-11

after calculation,

v= 11181.966 m/s

this is the speed required...for stone to escape the atmosphere.
So it is not possible.

[is this correct]

 

[D H]

Your question asks about throwing a stone "with sufficient energy escape the asteroid’s gravitational pull altogether", but your solution references the Earth's mass and radius. Are you sure you are using the correct mass and radius (the Earth is not an asteroid)?

 

[imy786]

density of asteroid is 4.0 × 10^3 kg m−3 (given in previous part of the quesiton).

desnisty= mass/volume

v= (4/3)*pi*R ^3...need R to calculate V

4.0 × 10^3 kg m−3 * v = m

using m and r of asteroid..i should be able to calculate escapte velocity .

[is this correct method]

 

[hage567]

I would think you should be able to determine the radius of the asteroid based on what you've done in the other parts of this question.

 

[ss612]

Radius calculation

can you explain how you calculated the radius of the asteroid?
cheers
ss