Solving Momentum Problems: Rocket, Crate & Cannon

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The discussion revolves around solving momentum problems involving a rocket explosion, two people jumping off a crate, and a cannon firing a shell. In the rocket problem, conservation of momentum was applied to find the third piece's velocity, resulting in a magnitude of 510 m/s. The crate scenario involved calculating the speed of the crate after two individuals jumped off, with initial calculations suggesting a speed of 36 m/s, but doubts were raised about the accuracy of the approach. Lastly, the cannon problem involves determining the distance between two fragments after an explosion, with the poster seeking guidance on calculating the y-component of momentum. The thread highlights challenges in applying conservation of momentum principles across different scenarios.
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1) Rocket fired up, when it reaches 300 m/s and 1000m, it explodes into three pieces. One contnues up at 450 m/s and the other continues east at 240 m/s. Third velocity?
used conservation of momentum with components
found that the velocity of the third piece had an x-component of -240 m/s and y-component of 450 m/s. solved and got 510 m/s. did i approach this problem correctly?
2) Two people standing on a crate on a frictionless frozen pond. One person weighs 75 kg, the other 45 kg and the crate 15 kg. They jump horizontaly from the top of the crate. Just after each jumps, the person moves away from the crate at 4 m/s relative to the crate.
a)What is the speed of the box if both jump off?
MVi = MVf
135(4) = 15(V)
V = 36 m/s
i have a feeling that i wdid that incorrectly
b)What is the speed the 75 kg jumps off and then the
45 kg person jumps off a few seconds later?
135(4) = 60V V= 9 velocity after one person
jumps
60(9) = 15V
V= 36
i also have a feeling that i did this one
incorrect since a and b are both the same
answer.
3)Cannon fires 100kg shell 60 degrees at 600 m/s. at highest point it explodes into two fragments (m1 = 2/5M and m2 = 3/5M), with an additional 10kJ of energy in the original horizontal direction. Whats the distance between the two pieces?
honestly for this one i am lost. i don't expect it to be solved, but could someone possible guide me through it? or get me started?
Thanks!
 
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First: x-component was correct but y is wrong.
 
can anyone give me a clue in finding the y-component?
 
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