Conservation of Linear Momentum

[skunk]

Homework Statement

A particle of mass 5m moving with speed v explodes and splits into two pieces with masses of 2m and 3m. The lighter piece continues to move in the original direction with speed 5v relative to the heavier piece. What is the actual speed of the lighter piece?

Homework Equations

Momentum = Mass x Velocity

The Attempt at a Solution

The answer is 4v, as stated in the answer sheet, but I've no idea how to get it. Appreciate any help here, thanks!

 

[PhanthomJay]

Start by writing the conservation of linear momentum equation.

 

[skunk]

I've only got: 5m x v = (2m x 5v) + (3m x -1 2/3 v)

Does the problem lie with the term "relative speed"?

 

[PeterO]

I've only got: 5m x v = (2m x 5v) + (3m x -1 2/3 v)

Does the problem lie with the term "relative speed"?

Certainly does!

 

[PhanthomJay]

I've only got: 5m x v = (2m x 5v) + (3m x -1 2/3 v)

Does the problem lie with the term "relative speed"?

Yes. You should always determine speeds with respect to the ground when using this equation. If the lighter piece is moving at 5v with respect to the heavier piece, and the heavier piece is moving at a speed v₂ with respect to the ground, then what is the speed of the lighter piece with respect to the ground, in terms of v and v₂?