Will Both Chunks of the Split Asteroid Miss Starbase Alpha?

[diablodude64]

An asteroid is spotted moving directly toward the center of Starbase Alpha. The frightened residents fire a missile at the asteriod, which breaks it into two chunks, one with 2.4 times the mass of the other. The chunks both pass the starbase at the same time. If the lighter chunk passes 1.8 km from one edge of the 2.2-km-wide starbase, will the other chunk hit or miss the starbase?

I am having some difficulty with this... I have attempted it multiple ways and still am unsure as to how to go about solving it.

 

[DukeLuke]

Can you post an attempt. Have you tried drawing a picture and writing conservation of momentum equations for the asteroid(s) before and after the rocket hits it.

 

[diablodude64]

Can you post an attempt. Have you tried drawing a picture and writing conservation of momentum equations for the asteroid(s) before and after the rocket hits it.

I have drawn a picture and used that for my attempts. I am using the center of mass equation. r(cm)=1/M(m1r1+m2r2...+mnrn)

 

[DaveC426913]

1] Why did you erase the template? It was there for a reason.
2] You still have not shown your attempt at an answer. The rules forbid us from helping you until you have done so.

 

[diablodude64]

1] Why did you erase the template? It was there for a reason.
2] You still have not shown your attempt at an answer. The rules forbid us from helping you until you have done so.

1] Because I didn't have the info that it asked for so I didn't think it was necessary.

2] I couldn't exactly write the graphs into here, as well as the 3 attempts/pages of work.

To sum, I figured it out.

Thanks for the help.

 

[skeptic2]

There doesn't seem to be enough information given to answer the problem. Although the relative masses of the pieces of asteroid are given, their diameters are not given. Since the deflected distances must be the centers of mass, depending on the size or diameters of the pieces, we still don't know if they will miss the spacebase or not.

 

[gneill]

There doesn't seem to be enough information given to answer the problem. Although the relative masses of the pieces of asteroid are given, their diameters are not given. Since the deflected distances must be the centers of mass, depending on the size or diameters of the pieces, we still don't know if they will miss the spacebase or not.

Depending upon the level of the course, the problem may only be looking for the edge-of-starbase to center-of-chunk spacing. Perhaps the original asteroid was only a few meters to a few tens of meters in diameter.

If you want to make things more complicated, assume a shape for the chunks and assume that they are composed of material of the same, uniform density. Densities in the range 3.3 to 4.5 g/cm³ are typical for such bodies.