A 780-kg two-stage rocket is traveling at a speed of 6.90×10 3 m/s away from Ear

Question

A 780-kg two-stage rocket is traveling at a speed of 6.90×103 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 2.10×103 m/s relative to each other along the original line of motion.

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

Express your answers using three significant figures separated by a comma.

2) 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

When the rocket splits we have two pieces with mass = 360 kg traveling at two different speeds with the same momentum

They each move (2100/2) = 1050 m/s = v from the original center of mass,

V1 = Vcm + v

V1= 6900+1050

V1= 7950 m/s

V2 = 6900 - 1050

V2= 5850 m/s
speed of each section (7950m/s , 5850 m/s)

speed of each section (7.95 x 103 m/s , 5.85 x 103 m/s)

Part B:
KE_i = ½*M*Vi2

KE_i = 8.5698 x 109 J

KE_f = {½*(M/2)*(V1²)} + {½*(M/2)*(V2²)}

KE_f = ½*(M/2)*(V1² + V2²)

KE_f = ½*(180)*(7950² + 5850²)

KE_f = 8.76825 x 109 J

E_explosion = KE_f – KE_i

E_explosion = 1.9845 x108 J

E_explosion = 1.98 x108 J

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