# 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.

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.

Expert's answer

Let's write the Momentum conservation law for the horizontal and vertical projections:

V: 3MV = MV

H: 0 = MV

where V = 277 m/s, V

Thus |V

V

V: 3MV = MV

_{1}+ MV_{3v}H: 0 = MV

_{2}+ MV_{3h}where V = 277 m/s, V

_{2}= 475 m/sThus |V

_{2}| = |V_{3h}| and |V_{3v}| = |3V-V_{1}|V

_{3}= √ (V_{3h}^{2}+ V_{3v}^{2}) = √ ( 475^{2}+ (3*277 - 212)^{2}) = 780.25Need a fast expert's response?

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