Final answer:
To find the total momentum of the three pieces after the explosion, we calculate the momentum of each piece individually and add them vectorially, considering their directions. However, we cannot provide a numerical answer without the direction of the third piece.
Step-by-step explanation:
The student's question regards the conservation of momentum in an explosive event. In such an event, the total momentum after the explosion must equal the total momentum before the explosion, which was zero since the hot pocket was initially at rest. To find the total momentum, we calculate the momentum of each individual piece and then vectorially add them.
The momentum of an object is given by the product of its mass (m) and velocity (v). Since the two pieces fly off at a 60-degree angle to each other, we have to consider the components of their velocities separately. For an angle θ, the components of velocity are v_x = v * cos(θ) and v_y = v * sin(θ).
A 20 mg piece moving at 20 m/s at some angle θ has a momentum of m*v = 0.020 kg * 20 m/s. A 30 mg piece moving at 12 m/s has a momentum of m*v = 0.030 kg * 12 m/s. The third piece, which we do not have an angle for, moves at 30 m/s.
The direction of the third piece can be determined by applying the conservation of momentum in both horizontal and vertical directions separately, as the momentum components must individually balance to maintain the initial momentum of zero. Calculations would involve using the provided angles and velocities, but as the question does not specify the direction of the third piece or the angles with respect to the horizontal or vertical, we cannot provide numerical values without this information.