Kinematics, Conservation of energy, momentum

[wcjy]

Homework Statement

An object of mass 8 kg explodes into two pieces at a height of 30 m from
the ground. Both small pieces fly out vertically. After 2 seconds of explosion, one
piece arrives the ground while the other piece is 16 m above the ground. Find the
mass of the small piece that hit the ground first.

Honestly i have no idea what type of question is this and how to approach this.

Relevant Equations

Kinetic energy = 0.5mv^2
Potential energy = mgh

m1 + m2 = 8
COE
0.5(m1)(u1)^2 + (m1)(g)(30) + 0.5(m2)(u2)^2 + (m2)(g)(30) = 0.5(m1)(v1)^2 + 0.5(m2)(v2)^2 + (m2)(g)(16)

Can you check if my eqn is correct? And can you advise what to do after this?
I wanted to do COLM but i don't know what is the initial part.

 

[haruspex]

Homework Statement:: An object of mass 8 kg explodes into two pieces at a height of 30 m from
the ground. Both small pieces fly out vertically. After 2 seconds of explosion, one
piece arrives the ground while the other piece is 16 m above the ground. Find the
mass of the small piece that hit the ground first.

Honestly i have no idea what type of question is this and how to approach this.
Relevant Equations:: Kinetic energy = 0.5mv^2
Potential energy = mgh

m1 + m2 = 8
COE
0.5(m1)(u1)^2 + (m1)(g)(30) + 0.5(m2)(u2)^2 + (m2)(g)(30) = 0.5(m1)(v1)^2 + 0.5(m2)(v2)^2 + (m2)(g)(16)

Can you check if my eqn is correct? And can you advise what to do after this?
I wanted to do COLM but i don't know what is the initial part.

That equation could be useful if you wanted to find the speed with which the small piece hit the ground, but you don't care about that.
What other conservation law might apply?

 

[wcjy]

That equation could be useful if you wanted to find the speed with which the small piece hit the ground, but you don't care about that.
What other conservation law might apply?

Conservation of momentum?

 

[haruspex]

Conservation of momentum?

Right. Across what event?

 

[wcjy]

Right. Across what event?

the explosion of the 8kg mass?

 

[haruspex]

the explosion of the 8kg mass?

Yes.

 

[wcjy]

Yes.

but i thought it does not have initial velocity so i can't apply it in the formula

 

[haruspex]

but i thought it does not have initial velocity so i can't apply it in the formula

The question as stated in post #1 does not make it clear, but you will have to assume zero initial velocity. Why is that a difficulty?

 

[wcjy]

The question as stated in post #1 does not make it clear, but you will have to assume zero initial velocity. Why is that a difficulty?

does that mean the eqn for colm is:
8*0 = m1(v1) + m2(v2)

 

[haruspex]

does that mean the eqn for colm is:
8*0 = m1(v1) + m2(v2)

Yes.