Conservation of Momentum (Explosion Kinematics)

[jay2001]

Homework Statement

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A 3200 kg space vehicle (including a launchable lifeboat) is traveling with a velocity of 300 m/s in a straight trajectory [East]. The lifeboat (200 kg) is fired at a speed of 1000 m/s [N of original trajectory].
a) After firing it is found that the horizontal component of each object’s velocity is still 300 m/s [along original trajectory]. Explain why.

Homework Equations

p = p'
p = mv

The Attempt at a Solution

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More of a theory question than problem solving... but I'm stumped on this. I feel like they shouldn't both have horizontal velocity components of 300 m/s - I believe that the lifeboat should have a velocity of 1000 m/s [N] (so a horizontal velocity component of zero), and the space vehicle would be redirected slightly South of East, so the horizontal velocity component would change from 300 m/s. Am I wrong, or just misunderstanding?

 

[haruspex]

I'm stumped on this

Think about what "north" and "east" etc. might mean in space.

Btw, you mean kinetics, not kinematics.

 

[ubergewehr273]

Make sure that you understand linear momentum conservation properly and come back to the question after thoroughly understanding the concept :)

 

[haruspex]

Make sure that you understand linear momentum conservation properly and come back to the question after thoroughly understanding the concept :)

I see no evidence that @jay2001 does not understand the concept, do you?

 

[PKM]

I believe that the lifeboat should have a velocity of 1000 m/s [N] (so a horizontal velocity component of zero)

Are you sure? Mind the lifeboat is moving along with the vehicle just before the launch.

and the space vehicle would be redirected slightly South of East, so the horizontal velocity component would change from 300 m/s.

The rocket can still redirect slightly South of East with the horizontal component of velocity fixed. What if the vertical component changes only? $\ddot\smile$

 

[Apashanka]

A 3200 kg space vehicle (including a launchable lifeboat) is traveling with a velocity of 300 m/s in a straight trajectory [East]. The lifeboat (200 kg) is fired at a speed of 1000 m/s [N of original trajectory].
a) After firing it is found that the horizontal component of each object’s velocity is still 300 m/s [along original trajectory]. Explain why.

From momentum conservation
p=p₁+p₂,
or,p²=p₁²+p₂²+
2p_1horizontalp₂
From energy conservation
p²/2m=p₁²/2m₁+p₂²/2m₂
Where p is the momentum of the system before disintegration and p₁ and p₂ are the momentum of the lifeboat and space vehicle respectively.

Now p,p_{1 horizontal},
p_1vertical and p₂ is given in the question.

 

[haruspex]

From momentum conservation
p=p₁+p₂,
or,p²=p₁²+p₂²+
2p_1horizontalp₂
From energy conservation
p²/2m=p₁²/2m₁+p₂²/2m₂
Where p is the momentum of the system before disintegration and p₁ and p₂ are the momentum of the lifeboat and space vehicle respectively.

Now p,p_{1 horizontal},
p_1vertical and p₂ is given in the question.

You do not appear to have understood the question. Nothing in your post helps.
Did you read post #2?

 

[Apashanka]

Think about what "north" and "east" etc. might mean in space

North and east only means the direction that are perpendicular to each other ,nothing to do with north and South in space.

 

[Apashanka]

Did you read post #2?

Yaa I have read it .
It only implies the mutually perpendicular direction ,nothing to confuse with the north and east of geography.

 

[Apashanka]

A 3200 kg space vehicle (including a launchable lifeboat) is traveling with a velocity of 300 m/s in a straight trajectory [East]. The lifeboat (200 kg) is fired at a speed of 1000 m/s [N of original trajectory].
a) After firing it is found that the horizontal component of each object’s velocity is still 300 m/s [along original trajectory]. Explain why.

To an observer who is sitting on the space vehicle he will see a horizontal velocity of lifeboat(being equal to that of space vehicle in the negative direction)as well as a vertical component of velocity of the lifeboat(given).
To an observer at absolute rest(reference frame) at the moment the life boat is launched he will see a horizontal component of velocity of lifeboat (being equal to that of space vehicle in the positive direction)and as well as vertical component of velocity of the lifeboat.(given).

 

[haruspex]

North and east only means the direction that are perpendicular to each other ,nothing to do with north and South in space.

and how might that relate to the "horizontal" information?
(Do you think you have an answer to the question posed?)

 

[Apashanka]

and how might that relate to the "horizontal" information?

Horizontal actually here may be referred to the plane in which the objects are moving or rather direction along the straight line of the motion as given in question ,and vertical refers perpendicular to this direction

 

[haruspex]

Horizontal actually here may be referred to the plane in which the objects are moving or rather direction along the straight line of the motion as given in question ,and vertical refers perpendicular to this direction

But how does that relate to the East and North references? Are you saying they are both horizontal?

 

[Apashanka]

But how does that relate to the East and North refernces? Are you saying they are both horizontal?

For an exm. you may take your right hand to be east direction and forehead to be north direction ,and space vehicle is moving along right hand and lifeboat is ejected along forehead.
Horizontal is along right hand and vertical is along forehead.

 

[Apashanka]

For an exm. you may take your right hand to be east direction and forehead to be north direction ,and space vehicle is moving along right hand and lifeboat is ejected along forehead.
Horizontal is along right hand and vertical is along forehead.

Or in 2-D Cartesian x is east(horizontal) and y is north (vertical).

 

[haruspex]

For an exm. you may take your right hand to be east direction and forehead to be north direction ,and space vehicle is moving along right hand and lifeboat is ejected along forehead.
Horizontal is along right hand and vertical is along forehead.

Yes, that's the key, but there was no hint of that in post #6.
Also, I feel the question setter had something a bit more specific in mind which would lead to that interpretation of how N and E relate to horizontal and vertical.