Three worked practice problems apply conservation of momentum to different collision scenarios: a 1D collision between two moving bodies, an explosion of a stationary body into two fragments, and a 2D collision where both bodies deflect at 45 degrees. Each scene states the setup, shows vector components, and walks through the algebra to find unknown final velocities. Useful for students reviewing momentum problem-solving strategies before exams or practicing vector decomposition in 2D collisions.
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Scene 4: Try It (a)On-Screen Title: Try It (a): 1D Linear CollisionQuestion: Body A of mass $2.0\text{ kg}$ moves in the positive direction at $4.0\text{ m/s}$, and body B of mass $3.0\text{ kg}$ moves in the negative direction at $4.0\text{ m/s}$ along a straight line. They collide. If body B's velocity after collision is $2.0\text{ m/s}$ in the positive direction, find body A's velocity after collision in $\text{m/s}$. Answer:$m_A v_{Ai} + m_B v_{Bi} = m_A v_{Af} + m_B v_{Bf}$ $(2.0)(4.0) + (3.0)(-4.0) = (2.0)v_{Af} + (3.0)(2.0)$ $-4.0 = 2.0 v_{Af} + 6.0 \implies 2.0 v_{Af} = -10.0$ $v_f = \mathbf{-5.0\text{ m/s}}$ Scene 5: Try It (b)On-Screen Title: Try It (b): Stationary Body ExplosionQuestion: A stationary body of mass $8.0\text{ kg}$ breaks into body A ($3.0\text{ kg}$) and body B ($5.0\text{ kg}$). If body A moves left at $10\text{ m/s}$ after the collision, find body B's velocity and direction after collision. Answer:$0 = m_A v_{Af} + m_B v_{Bf}$ $0 = (3.0)(-10) + (5.0)v_{Bf}$ $5 v_{Bf} = 30 \implies v_{Bf} = \mathbf{+6\text{ m/s}}$ Direction: Right (opposite to A). Scene 6: Try It (c)On-Screen Title: Try It (c): 2D Collision at $45^\circ$Question: On a smooth horizontal surface, body A ($1.0\text{ kg}$) moving at $4.0\text{ m/s}$ collides with stationary body B ($2.0\text{ kg}$). After collision, A deflects $45^\circ$ above the horizontal and B deflects $45^\circ$ below the horizontal. Find the final speeds of A and B. Answer:$v_{Bf} = \mathbf{1.41\text{ m/s}}$ ($\sqrt{2}$) $v_{Af} = \mathbf{2.83\text{ m/s}}$ ($2\sqrt{2}$) IMPORTANT LANGUAGE RULE: All on-screen text must be in Arabic EXCEPT mathematical equations, formulas, laws, symbols, variables, and numerical expressions. Keep every equation, formula, and law exactly as provided, without translating or changing it. Translate only the explanatory text, headings, labels, and descriptions into Arabic. Arabic text must use proper RTL direction and correct Arabic typography. Do not use English text anywhere else on the screen. Audience: student