Mass per unit volume i hope it helps
Momentum will be conserved in one dimension in the explosion.
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Given that the fragment a acquires three
times the kinetic energy of the fragment b.
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P</span><span><span>initial </span><span>= p</span></span>final ⇒ 0 =mₐv⁰ₐ+mьv⁰ь= 0 ⇒ v⁰ь = -mₐv⁰ₐ/mь
KE= 3KEь
⇒1/2 mₐv⁰ₐ² = 3 (1/2mьv⁰ь²)
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⇒1/2 mₐv⁰ₐ² = 3/2 mь(-mₐv⁰ₐ/mь)²
⇒1/2 mₐv⁰ₐ² = 3/2 mь(mₐ²v⁰ₐ²/mь²)
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⇒1/2 x 2/3 = mₐ/mь= 1/3
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Thus the ratio
of the masses of the fragments is 1:3.
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Momentum is conserved, so the sum of the separate momenta of the car and wagon is equal to the momentum of the combined system:
(1250 kg) ((36.2 <em>i</em> + 12.7 <em>j </em>) m/s) + (448 kg) ((13.8 <em>i</em> + 10.2 <em>j</em> ) m/s) = ((1250 + 448) kg) <em>v</em>
where <em>v</em> is the velocity of the system. Solve for <em>v</em> :
<em>v</em> = ((1250 kg) ((36.2 <em>i</em> + 12.7 <em>j </em>) m/s) + (448 kg) ((13.8 <em>i</em> + 10.2 <em>j</em> ) m/s)) / (1698 kg)
<em>v</em> ≈ (30.3 <em>i</em> + 12.0 <em>j</em> ) m/s
I think it would be eager
