Answer :
Final answer:
The kinetic energy of the 6 kg piece is calculated using the conservation of momentum to find its velocity and then applying the kinetic energy formula, resulting in 192 J. the correct answer is c.
Explanation:
The problem involves an explosion that follows the law of conservation of momentum. Because the total momentum before and after the explosion must be equal, we can calculate the velocity of the 6 kg piece if we are given the velocity of the 3 kg piece. In this question, the 3 kg piece has a velocity of 16 m/s. Since there are only two pieces and no external forces, the momentum of the 3 kg piece is equal and opposite to the momentum of the 6 kg piece.
To find the velocity of the 6 kg piece, we use the formula for conservation of momentum: m1 * v1 = -m2 * v2 Filling in what we know: 3 kg * 16 m/s = -6 kg * v2, we find that v2 = -8 m/s (the negative sign indicates it is moving in the opposite direction to the 3 kg piece). To find the kinetic energy of the 6 kg piece, we use the formula: KE = 0.5 * m * v^2 Substituting in the mass and velocity of the 6 kg piece: KE = 0.5 * 6 kg * (-8 m/s)^2 = 192 J.
