A fireworks rocket is launched vertically into the night dkywith an initial spee

Question

A fireworks rocket is launched vertically into the night dkywith an initial speed of 47.6m/s. The rocket coasts after beinglaunched, then explodes and breaks into 2 pieces of equal mass 3slater. A. If each piece follows the trajectory that is initially 50degrees to the vertical, what was theri speed immediately after theexplosion? B. What is the velocity of the rocket's center of mass beforethe explosion? C. What is the velocity of the rocket's center of mass afterexplosion? D. What is the acceleration of the rocket's center of massbefore the explosion? E. What is the acceleration of the rocket's center of massafter the explosion? A fireworks rocket is launched vertically into the night dkywith an initial speed of 47.6m/s. The rocket coasts after beinglaunched, then explodes and breaks into 2 pieces of equal mass 3slater. A. If each piece follows the trajectory that is initially 50degrees to the vertical, what was theri speed immediately after theexplosion? B. What is the velocity of the rocket's center of mass beforethe explosion? C. What is the velocity of the rocket's center of mass afterexplosion? D. What is the acceleration of the rocket's center of massbefore the explosion? E. What is the acceleration of the rocket's center of massafter the explosion?

Explanation / Answer

A fireworks rocket is launched vertically into the night dkywith an initial speed of 47.6m/s. The rocket coasts after beinglaunched, then explodes and breaks into 2 pieces of equal mass 3slater. A. If each piece follows the trajectory that is initially 50degrees to the vertical, what was their speed immediately after theexplosion?
>>> 3 sec later, speed is
v = 47.6 - gt = 47.6 - 9.8*3 = 18.3 m/s
if mass of rocket is m,
before explosion: vertical momentum Py = mv, horizontal momentum Px= 0
since it breaks into 2 equal pieces, each has mass m/2 and speed V(say).
after explosion: vertical momentum = Py' = 2*(m/2)Vcos(50),horizontal = 0
momentum conservation gives
mv = mV cos(50)
V = v/cos(50) = 18.3/cos(50) = 28.5 m/s
B. What is the velocity of the rocket's center of mass beforethe explosion?
>>> v = 18.3 m/s
C. What is the velocity of the rocket's center of mass afterexplosion?
>>> same v = 18.3 m/s
D. What is the acceleration of the rocket's center of massbefore the explosion?
>>> -g = -9.8 m/s^2
E. What is the acceleration of the rocket's center of massafter the explosion?
>>> -g = -9.8 m/s^2

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