Answer to Question #1182 in Mechanics | Relativity for Jon Allen

Question #1182
A rocket is fired vertically upward.& At theinstant it reaches an altitude of 1630 m and a speed of 277 m/s, it explodes into three equal fragments.& One fragment continues to moveupward with a speed of 212 m/s following the explosion.& The second fragment has a speedof 475 m/s and is moving east right after the explosion.& What is the magnitude of the velocity ofthe third fragment? Answer in units of m/s.
1
Expert's answer
2010-12-22T07:18:11-0500
Let's write the Momentum conservation law for the horizontal and vertical projections:
V: 3MV = MV1 + MV3v
H: 0 = MV2 + MV3h
where V = 277 m/s, V2 = 475 m/s
Thus |V2| = |V3h| and |V3v| = |3V-V1|
V3 = √ (V3h2 + V3v2) = √ ( 4752 + (3*277 - 212)2) = 780.25

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