The velocity of piece C is -10.2 m/s, indicating that it is moving in a direction opposite to that of piece A and piece B.
To determine the velocity of piece C, we can apply the principle of conservation of momentum. The total momentum of the system before the explosion must be equal to the total momentum of the system immediately after the explosion.
Step 1: Identify the Initial Momentum
Before the explosion, the model rocket is at rest, so its initial momentum is zero.
Step 2: Calculate the Momentum of Pieces A and B
The momentum of piece A is given by:
pA = mA * vA
where:
pA is the momentum of piece A (kg m/s)
mA is the mass of piece A (122.5 g = 0.1225 kg)
vA is the velocity of piece A (1.45 m/s)
pA = (0.1225 kg)(1.45 m/s) ≈ 0.179 kg m/s
The momentum of piece B is given by:
pB = mB * vB
where:
pB is the momentum of piece B (kg m/s)
mB is the mass of piece B (20.0 g = 0.020 kg)
vB is the velocity of piece B (7.40 m/s)
vB = 7.40 m/s * cos(-30°) = 6.35 m/s
pB = (0.020 kg)(6.35 m/s) ≈ 0.127 kg m/s
Step 3: Set Up the Equation for Conservation of Momentum
The total momentum of the system immediately after the explosion can be expressed as:
0 = pA + pB + pC
where:
pC is the momentum of piece C (kg m/s)
Substituting the values we calculated earlier, we get:
0 = 0.179 kg m/s + 0.127 kg m/s + pC
Solving for pC, we get:
pC = -0.306 kg m/s
Since the negative sign indicates a direction opposite to that of piece A and piece B, the velocity of piece C is:
vC = pC / mC = (-0.306 kg m/s) / (0.030 kg) ≈ -10.2 m/s
Therefore, the velocity of piece C is -10.2 m/s, indicating that it is moving in a direction opposite to that of piece A and piece B.