Let's break down the problem step by step: --- ## **Step 1: Given Data** - **Total mass of firecracker, \( m_{\text{total}} \) = 220 g = .220 kg** - **Mass of one piece, \( m_1 \) = 91 g = .091 kg** - **Velocity of the 91 g piece, \( v_1 \) = 15 m/s** (direction given as downward) - **Mass of the other piece, \( m_2 \) is unknown** - **Velocity of the other piece, \( v_2 \) is unknown** --- ## **Step 2: Conservation of Momentum** **Before explosion:** - The firecracker is at rest, so total momentum = ****. **After explosion:** - Two pieces move in opposite directions. Let’s assume **up** is positive and **down** is negative (since the 91 g piece goes down, its velocity will be **-15 m/s**). \[ \text{Total momentum after explosion} = \] \[ m_1 v_1 + m_2 v_2 = \] --- ## **Step 3: Find the Unknown Mass** \[ m_2 = m_{\text{total}} - m_1 = .220\,\text{kg} - .091\,\text{kg} = .129\,\text{kg} \] --- ## **Step 4: Solve for the Unknown Velocity** Using the momentum equation: \[ m_1 v_1 + m_2 v_2 = \] \[ (.091\,\text{kg})(-15\,\text{m/s}) + (.129\,\text{kg})(v_2) = \] \[ -1.365 + .129 v_2 = \] \[ .129 v_2 = 1.365 \] \[ v_2 = \frac{1.365}{.129} \] \[ v_2 \approx 10.6\,\text{m/s} \quad (\text{upward, since it's positive}) \] --- ## **Step 5: Final Answers** - **Mass of the second piece:** \[ \boxed{.129\,\text{kg} \text{ or } 129\,\text{g}} \] - **Velocity of the 91 g piece:** \[ \boxed{-15\,\text{m/s} \text{ (downward)}} \] - **Velocity of the 129 g piece:** \[ \boxed{10.6\,\text{m/s} \text{ (upward)}} \] --- ### **Summary Table** | Piece | Mass (g) | Velocity (m/s) | Direction | |:-------------:|:--------:|:--------------:|:---------:| | 1 (given) | 91 | -15 | Down | | 2 (unknown) | 129 | +10.6 | Up | --- If you need the kinetic energy or any additional information, let me know!