Can the Crew's Plan to Fragment an Asteroid Succeed?

[phalanx123]

Hi I got this question, it looks like its simple. But I don't know if I've done it right or not? Please help me check it.

A 2kg rock is heading straight for a space station at a speed of 100 m/s. The crew plan to break the rock up into small fragments by hitting it with a rocket of 3kg traveling at 1000 m/s. If it takes 1.0 *10^6 J to fragment the rock, show wether or not their plan can succeed. (Speed are given in the station' s frame.



I simply said that the rocket will have a kinetic energy of 1/2mv^2=1/2*3*1000^2=1.25*10^6 J. SO this is higher than the minimum energy required to break the rock, so the plan will work.

But it is so simple I think I've missed some information heere. Could somebody give me a little help please? Thank you

 

[HallsofIvy]

Although I imagine the answer would still be "yes", not that the 1000 m/s you use for the rocket's velocity is relative to the space station not the asteroid. Of course, it is the rocket's velocity relative to the asteroid that will be converted into energy to break it apart. If the rocket is going 1000 m/s directly away from the space station, and the asteroid is going 100 m/s directly toward the space station, what is the rocket's speed relative to the asteroid?

 

[phalanx123]

Oh I see, so I have to use 1100 m/s instead of 1000 m/s. Ah that makes more sense. Thank you very much. I am also wondering if it's correct to do it this way: calculate the rocket's kinetic energy relative to the station first then take away the kinetic energy of the rock relative to the station from the rocket's kinetic energy? Anybody got any ideas? Thanks.