Meteorite heading towards earth

[josephcollins]

Hi ppl. I have a short question. A meteorite of mass m has a velocity u=2.00*10^4 m/s when it is at an infinite distance from the earth. It eventually collides with the eath with a velocity v. Calculate v. given are the radius of earth(6.37*10^6m) and go=9.80Nkg^-1)

I used the argument that the change in kinetic energy is going to be equal to 0.5m(v^2-u^2) which also equals GMem/2Re which resolves to goRem/2. Equating and calculating gives 2.15*10^4m/s. Could someone verify that this is correct and that potential energy or total energy is not neglected in my reasoning? thanks, joe

 

[Doc Al]

I used the argument that the change in kinetic energy is going to be equal to 0.5m(v^2-u^2) which also equals GMem/2Re which resolves to goRem/2.

I don't see why you divided by 2. (The change in PE should equal $g R_e m$)

 

[DaveC426913]

Wow! That meteorite had quite the bounce to it to achieve that high and fast of an arc, don't you think?

Or perhaps your prof meant meteor?

;)

 

[Doc Al]

I'll bet the prof meant meteoroid on its way to becoming a meteorite. (If the meteoroid burns up--becoming a "shooting star"--then it would be a meteor.)

Regardless, that's one heck of a meteoroid to make it through the atmosphere with no apparent loss of mass.

 

[curvedlogic]

Most scenarios seem to imply that massive objects hitting our planet would be traveling at a speed that would give days if not weeks of warning.

Is there any reason that a meteor should not hit the Earth at a very high relative velocity? Even one traveling at 80% the speed of light would be difficult to see coming, and hence be something of a surprise!