A 950-kg two-stage rocket is traveling at a speed of 6.95×10 3 m/s away from Ear

Question

A 950-kg two-stage rocket is traveling at a speed of 6.95×103 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 2.80×103 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? (va, vb = ____ m/s). Part B) How much energy was supplied by the explosion? [Hint: What is the change in kinetic energy as a result of the explosion?] (deltaK = _____J).

Explanation / Answer

Mass of the whole system M=950kg

Initial velocity V = 6950m/s

from the given dat it is clear that the rocket is separated into two equal parts after explosion.

a) hence speed of each section after explosion = relative velocity/2

=2800/2

= 1400 m/s

b) velocity of first part v1 = v + 1400 =6950 +1400 = 8350 m/s

velocity of the second part v2 = V-1400 =6950 -1400 =5550 m/s

Kinetic energy of the first part K1 = 1/2 mv21

= 1/2 *950/2 * (8350)2

=1.66 * 1010 j

Kinetic energy of the second part K2 = 1/2 mv22

= 0.5* 950/2 * (5550)2

   = 0.731 * 1010j

Energy supplied by the collissio = change in kinetic energy

=( 1.66 - 0.731)* 1010 J

= 0.929 *1010 J

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