A 795-kg two-stage rocket is traveling at a speed of 6.60×103 m/s away from Eart

Question

A 795-kg two-stage rocket is traveling at a speed of 6.60×103 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 2.90×103 m/s relative to each other along the original line of motion.

A) What is the speed of each section (relative to Earth) after the explosion?

B) How much energy was supplied by the explosion? [Hint: What is the change in kinetic energy as a result of the explosion? Express your answer to three significant figures and include the appropriate units.

Explanation / Answer

a) take rocket as a frame of ref.

Initial momentum = 0

By conservation of momentum

Speed of each secion = 2900 / 2 = 1450 m/s

Velocity of Upper section = 1450 m/s

Velocity of lower section = -1450 m/s

Vu = 6600 + 1450 = 8050 m/s

Vl = 6600 - 1450 = 5150 m/s

b) KEi = 0.5mv^2 = 0.5*795*6600^2 = 1.7315*10^10 J

KEf = (0.5*397.5*8050^2) + (0.5*397.5*5150^2) = 1.815*10^10 J

KE released = KEf - KEi = 8.36*10^8 J

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