You release a 3-kg firecracker from rest. At t = 0.4 s, the firecracker is moving downward with speed 4 m/s. At this same instant, the firecracker begins to explode into two pieces with masses mtop = 1 kg and mbottom = 2 kg. At the end of the explosion (t = 0.8 s), the top piece is moving upward with speed 4 m/s.Determine the velocity of the bottom piece at t = 0.8 s.(Hints: Make a momentum vector diagram. Don’t forget to include impulse in your diagram!) **Title: Understanding Conservation of Momentum Through Collision Problems**---**Introduction:**This educational resource aims to explain the concept of momentum conservation in a system involving two objects. The example involves a mass initially moving as a single unit that splits into two separate masses. By analyzing the change in momentum, we determine an unknown velocity after the split.**Diagram Explanation:****Initial State (t = 0.4 s):**- **Mass Details:** - Combined Mass (m) = 3 kg- **Velocity:** - Initial Velocity (|v|) = 4 m/s (downward direction)- **Visual:** - A single rectangle representing the combined mass of 3 kg moving downward.**Final State (t = 0.8 s):**- **Mass Details:** - Top Mass (m_top) = 1 kg - Bottom Mass (m_bottom) = 2 kg- **Velocity:** - Velocity of Top Mass (|v_top|) = 4 m/s (upward direction) - Velocity of Bottom Mass (v_bottom) = ?- **Visual:** - Two separate rectangles. The top rectangle represents the 1 kg mass moving upward, and the bottom rectangle represents the 2 kg mass with an unknown velocity downward.**Key Inquiry:**What is the velocity of the bottom mass (\(v_{bottom}\))?**Understanding Through Physics Concepts:**The principle of conservation of momentum states that the total momentum of a closed system remains constant if no external forces act on it. Given:- Initial Momentum (P_initial) = \(m \cdot v = 3 \, \text{kg} \cdot 4 \, \text{m/s} = 12 \, \text{kg} \cdot \text{m/s}\) (downward direction)- Final Momentum (P_final) = \(m_{top} \cdot v_{top} + m_{bottom} \cdot v_{bottom}\)Since the momenta in opposite directions can be considered, we set up the equation considering the directions:\[P_{initial} = P_{final}\]\[3 \,\text{kg} \cdot 4 \,\text{m/s} = 1 \,\text{kg} \cdot 4 \,\text{m/s} - 2 \,\

Name: You release a 3-kg firecracker from rest. At t = 0.4 s, the firecracke
Uploaded: 2024-03-20T06:57:37.000Z
Channel: Bartleby
Description: You release a 3-kg firecracker from rest. At t = 0.4 s, the firecracker is moving downward with speed 4 m/s. At this same instant, the firecracker begins to explode into two pieces with masses mtop = 1 kg and mbottom = 2 kg. At the end of the explosi