A 975-kg two-stage rocket is traveling at a speed of 6.50×10 3 m/s away from Ear

Question

A 975-kg two-stage rocket is traveling at a speed of 6.50×103 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 3.00×103 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.

B

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

Explanation / Answer

M = 975 kg, v = 6.50 * 103 m/s

m1 = 975 / 2 = 487.5 kg, m2 = 975/2 = 487.5 kg

v1 - v2 = 3.00 * 103 m/s

a) From moment of conservation

M V = m1 v1 + m2 v2

975 * 6.50 * 103 = 487.5 * [(3.00 * 103) + v2 + v2]

13000 = (3.00 * 103) + 2 v2

v2 = 5000 m/s, v1 = 8000 m/s

b) Energy supplied = [(1/2 m1 v12) + (1/2 m2 v22)] - [1/2 MV2]

= 1097 * 106 m/s

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