Question

A 770-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 2.60×103 m/s relative to each other along the original line of motion.What is the speed of each section (relative to Earth) after the explosion?How much energy was supplied by the explosion?

Answer 1

Step-by-step explanation:

Let's just have our reference frame travel along with the original un broken mass. This way the original velocity is not relevant.

Each half will have a mass of 770/2 = 385 kg

Each half will have the same magnitude of velocity (conservation of momentum) which will be 2.6 x 10³/2 = 1.30 x 10³ m/s

Now add back the reference frame velocity to get velocity relative to earth.

Section one will have velocity 6.90 x 10³ + 1.30 x 10³ = 8.2 x 10³ m/s

Section two will have velocity 6.90 x 10³ - 1.30 x 10³ = 5.6 x 10³ m/s

In the moving reference frame, each half will have kinetic energy which could only come from the explosion

KE = ½(385)(1.3 x 10³)² = 325,325,000 J

2(325,325,000) = 650,650,000 J released in the explosion.

Rounding to the three significant figures of the problem numerals

E = 6.50 x 10⁸ J or 650 MJ released