1. Conservation of Momentum
* Before the explosion: The asteroid has a momentum of (mass * velocity) = 13 kg * 110 m/s = 1430 kg*m/s.
* After the explosion:
* Piece 1 (at rest): momentum = 0
* Piece 2 (same velocity): momentum = (13 kg / 3) * 110 m/s = 476.67 kg*m/s
* Piece 3 (unknown velocity): momentum = (13 kg / 3) * v3
Since momentum is conserved, the total momentum before equals the total momentum after:
1430 kg*m/s = 0 + 476.67 kg*m/s + (13 kg / 3) * v3
Solving for v3:
v3 = (1430 - 476.67) * (3 / 13) = 273.33 m/s
2. Kinetic Energy
* Before the explosion: Kinetic energy = (1/2) * mass * velocity^2 = (1/2) * 13 kg * (110 m/s)^2 = 78650 J
* After the explosion:
* Piece 1: Kinetic energy = 0
* Piece 2: Kinetic energy = (1/2) * (13 kg / 3) * (110 m/s)^2 = 25216.67 J
* Piece 3: Kinetic energy = (1/2) * (13 kg / 3) * (273.33 m/s)^2 = 51433.33 J
3. Energy of Explosion
The energy of the explosion is the difference between the total kinetic energy after the explosion and the kinetic energy before the explosion:
Energy of explosion = (25216.67 J + 51433.33 J) - 78650 J = -1999.99 J
Note: The negative sign indicates that the total kinetic energy *decreased* after the explosion. This is expected, as some of the initial kinetic energy was converted into other forms of energy during the explosion (like heat and sound).
Therefore, the energy of the explosion is approximately 2000 J.
