Conservation of Momentum of Rocket Exploding after Takeoff

In summary, the conversation discussed solving for the speed and distance of a moving object before and after an explosion using equations. The topic of finding initial velocity was also mentioned, as well as determining masses based on a given ratio. The direction of movement was also considered.
  • #1
hisiks
6
0
Homework Statement
A 1500 kg weather rocket accelerates upward at 10.0 m/s^2. It explodes 2.00 s after liftoff and
breaks into fragments. One piece is twice as massive as the other. Photos reveal that the
lighter fragment travelled straight up and reached a maximum height of 530 m. What was the
speed and direction of the heavier fragment just after the explosion?
Relevant Equations
pi = pf
m1v1i + m2v1i = m1v2f + m2v2f
vf = vi +at
d = vit + 1/2at^2
vf^2 = vi2 + 2ad
PEi + KEi = PEf + KEf
-Solved for vf using equation 3 to get 20.0m/s (speed before explosion) then solved for the distance to reach the explosion using equation 4, to get 20.0m, which felt wrong having the same numbers but that may just be coincidence.
-Found the distance travelled of the lighter piece using 530m - 20.0m to get 510m travelled after the explosion.
-Stuck trying to use equation 6 to find inital velocity.
Stuck with the remainder of the question.

EDIT: Found masses using Mtotal = m1 + m2, & m2 = 2m1, thefore m1 = 500kg and m2 = 1000kg.
 
Last edited:
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  • #2
hisiks said:
that may just be coincidence
It's because the time is 2 seconds and ##\frac 122^2=2##.
hisiks said:
Found masses
The actual masses are irrelevant, unless another part of the question asked for them. The given ratio is all you need.
What did you get for the speed and direction of the heavier portion?
 
  • #3
haruspex said:
It's because the time is 2 seconds and ##\frac 122^2=2##.

The actual masses are irrelevant, unless another part of the question asked for them. The given ratio is all you need.
What did you get for the speed and direction of the heavier portion?
This is what I came up with for a speed, however I'm not particularly confident in it. As for the direction, would it just be down?
 

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  • #4
hisiks said:
This is what I came up with for a speed, however I'm not particularly confident in it. As for the direction, would it just be down?
Looks right.
 
  • #5
haruspex said:
Looks right.
Would you agree the direction would just be down as well?
 
  • #6
hisiks said:
Would you agree the direction would just be down as well?
yes
 

1. How does the conservation of momentum apply to a rocket exploding after takeoff?

The conservation of momentum states that the total momentum of a closed system remains constant, meaning that the initial momentum before an event must equal the final momentum after the event. In the case of a rocket exploding after takeoff, the initial momentum of the rocket and its fuel must equal the final momentum of the debris and gases after the explosion.

2. What factors affect the conservation of momentum in a rocket explosion?

The conservation of momentum in a rocket explosion is affected by various factors such as the mass and velocity of the rocket and its fuel, the direction and magnitude of the explosion, and any external forces acting on the system.

3. How does the conservation of momentum affect the trajectory of the debris after a rocket explosion?

The conservation of momentum dictates that the total momentum of the system must remain constant. This means that the trajectory of the debris after a rocket explosion will be affected by the initial momentum of the rocket and its fuel, as well as any external forces acting on the system.

4. Can the conservation of momentum be violated in a rocket explosion?

No, the conservation of momentum is a fundamental principle in physics and cannot be violated. This means that the total momentum of the system must remain constant, even in the event of a rocket explosion.

5. How does the conservation of momentum impact rocket design and safety?

The conservation of momentum plays a crucial role in rocket design and safety. Engineers must carefully consider the distribution of mass and velocity in a rocket to ensure that the conservation of momentum is maintained throughout the flight and in the event of an explosion. This helps to prevent accidents and ensure the safety of astronauts and equipment on board.

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