A 770-kg two-stage rocket is traveling at a speed of 6.30×10 3 m/s away from Ear

Question

A 770-kg two-stage rocket is traveling at a speed of 6.30×103 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 2.60×103 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)

What are the direction of each section (relative to Earth) after the explosion?

What are the direction of each section (relative to Earth) after the explosion?

(c) one away from Earth and the other towards the Earth

(c)

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

(c) one away from Earth and the other towards the Earth

(c)

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

Explanation / Answer

a) V1 = 6.3E3 + ½(2.6E3) = 7.6E3 m/s
.....V2 = 6.3E3 - ½(2.6E3) = 5E3 m/s

Note that their separation velocity = 2600 m/s

b), both are still headed away from earth (v > 0)

c) initial KE = ½ *770kg * (6300m/s)² =1.53e10 J
final KE = ½ * (770kg/2) * (7600² + 5000²)m²/s² = 1.593e10 J
supplied energy = 6.91e8 J = 691 MJ

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