A 800-kg two-stage rocket is traveling at a speed of 6.70×103 m/s away from Eart

Question

A 800-kg two-stage rocket is traveling at a speed of 6.70×103 m/s away from Earth when a predesigned explosion separates the rocket into two sections of equal mass that then move with a speed of 2.70×103 m/s relative to each other along the original line of motion.

Part A:

What is the speed of each section (relative to Earth) after the explosion? Enter your answers numerically separated by a comma.

va, vb =

Part B:

How much energy was supplied by the explosion? [Hint: What is the change in kinetic energy as a result of the explosion?]

K =

Explanation / Answer

  (A) Apply conservation of momentum:

M*V = m1*v1 * m2*v2
and v1-v2 = 2.00×10^3

=> 800*6.7×10^3 = (800/2)* (2.7×10^3 +v2) + (800/2)*v2

= 5360000 = 1080000+400v2+400v^2

= 4280000 = 400v2+400v^2
=> v2 = 1.029x10^3 m/s
=> v1 = 1.03x10^3m/s

KEi = ½MVi² =1.7956E10 J

KEf = ½(M/2)*1.029x10^3² + 1.03x10^3²) = 4.23*E8 J

b) Eex = KEf - KEi = 7.533E6 J

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