A 800-kg two-stage rocket is traveling at a speed of 6.20×10 3 m/s away from Ear
ID: 1603346 • Letter: A
Question
A 800-kg two-stage rocket is traveling at a speed of 6.20×103 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.
Part A
What is the speed of each section (relative to Earth) after the explosion?
Enter your answers numerically separated by a comma.
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Part B
How much energy was supplied by the explosion? [Hint: What is the change in kinetic energy as a result of the explosion?]
A 800-kg two-stage rocket is traveling at a speed of 6.20×103 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.
Part A
What is the speed of each section (relative to Earth) after the explosion?
Enter your answers numerically separated by a comma.
va, vb = m/sSubmitMy AnswersGive Up
Part B
How much energy was supplied by the explosion? [Hint: What is the change in kinetic energy as a result of the explosion?]
K = JExplanation / Answer
Total Mass of the rocket = 800 kg
Mass of each section = m1=m2= = 800 /2 =400 Kg
Intial speed of rocket =V = 6.20×103 m/s
relative velocity of two sections= v1 - v2 = 2.60×103 m/s
(a) according to the conservation of linear momentum,
M V = m1v1 + m2 v2
v1-v2=2.6x103
v1=v2+2.6x103
800 x 6.20×103 = (400) [(2.60×103 +v2) + v2 ]
12400 = 2 v2 + 2600
v2 = 4900 m/s
v1 = 2.50×103 m/s + v2
v1 = 2500+4900
v1=7400 m/s.
(b) Energy supplied by explosion =Final kinetic energy - initial kinetic Energy before explosion
E = [ (1/2)m1v12 + (1/2)m2v22 ]- [(1/2)MV2]
= (1/2 )[(400)(7400)2+ (400)(4900)2] - [(1/2)(800)(6200)2]
= 3.78 x 108 J
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