- #1
2sonian
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I'm running into trouble how to conceptualize and determine my reference frames to make the solving of this problem easy:
It's a variation on the "exploding shell" problem, except that an intial velocity of 300 m/s is given to the particle. Here's the setup:
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A plane has exploded into three pieces. At the instant of the explosion, the plane was flying at an altitude of 1808 ft (551.079 m) at 671.08 mph (300.000 m/s) heading due north.
Two pieces of the plane were recovered.
Half the plane was recovered 5000 meters due north of the explosion point
One quarter of the plane was recovered 3000 meters away from the explosion point, at a compass heading of 240° (i.e. 60° south of due east from the explosion point)
Each piece was found at an elevation of approx. 200ft, due to the topography of the area, you can assume that the last piece will be found at a similar elevation.
It is believed that the plane broke up into only three pieces, so only one piece is left. Using the information given, can you find the last piece?
Based on the reports at the time, it was a calm, clear windless day and due to the special nature of the plane, wind resistane is not a factor, and all three pieces impacted simultaneously.
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So I figured that it took 10.0012 seconds for the pieces to impact the ground, but am not sure why I would need to know this at all.
I generally am thinking that this is a conservation of linear momentum problem. I that I could take the two momentum vectors (the one due north and the southeasterly one) and sum them together and then add a third one so I get the overall momentum to be zero. The magnitude and the direction of this third vector, would seem to me to necessarily be symmetrical to the southeasterly momentum vector since the first vector lands along the same line of flight as before the explosion.
Something in the back of my mind says this is too simple an approach and that I'm missing something here.
Any ideas on how to get this set up properly and determine the final piece location?
Thanks
2sonian
It's a variation on the "exploding shell" problem, except that an intial velocity of 300 m/s is given to the particle. Here's the setup:
--------------------------------------------
A plane has exploded into three pieces. At the instant of the explosion, the plane was flying at an altitude of 1808 ft (551.079 m) at 671.08 mph (300.000 m/s) heading due north.
Two pieces of the plane were recovered.
Half the plane was recovered 5000 meters due north of the explosion point
One quarter of the plane was recovered 3000 meters away from the explosion point, at a compass heading of 240° (i.e. 60° south of due east from the explosion point)
Each piece was found at an elevation of approx. 200ft, due to the topography of the area, you can assume that the last piece will be found at a similar elevation.
It is believed that the plane broke up into only three pieces, so only one piece is left. Using the information given, can you find the last piece?
Based on the reports at the time, it was a calm, clear windless day and due to the special nature of the plane, wind resistane is not a factor, and all three pieces impacted simultaneously.
---------------------------------
So I figured that it took 10.0012 seconds for the pieces to impact the ground, but am not sure why I would need to know this at all.
I generally am thinking that this is a conservation of linear momentum problem. I that I could take the two momentum vectors (the one due north and the southeasterly one) and sum them together and then add a third one so I get the overall momentum to be zero. The magnitude and the direction of this third vector, would seem to me to necessarily be symmetrical to the southeasterly momentum vector since the first vector lands along the same line of flight as before the explosion.
Something in the back of my mind says this is too simple an approach and that I'm missing something here.
Any ideas on how to get this set up properly and determine the final piece location?
Thanks
2sonian