Two trolleys are rolling towards each other and they collide. Trolley A has a mass of 6.5 kg and Trolley B has a mass of 29.8 kg. Before the collision, Trolley A was moving East at 13.6 m s-1 and Trolley B was moving West at 17.8 m s-1. After the collision, trolley B slows down to one quarter of its original speed while trolley A reverses direction. What is the final velocity of trolley A?

Question

BlackTom AI · Accepted Answer

Conservation of linear momentum applies: m_A v_A,i + m_B v_B,i = m_A v_A,f + m_B v_B,f.

1) Relevant knowledge points and concepts
- Linear momentum (p = m v) is conserved for the two-trolley system during the collision (no external horizontal forces).
- Choose East as positive and West as negative. Reversal of A means its final velocity will be negative (West). B “slows to one quarter of its original speed” means its final speed = (1/4)(17.8 m/s) = 4.45 m/s and it remains West (negative).

2) Step-by-step reasoning and calculations
- Given: m_A = 6.5 kg, v_A,i = +13.6 m/s; m_B = 29.8 kg, v_B,i = −17.8 m/s.
- Final for B: v_B,f = −(1/4)(17.8) = −4.45 m/s. Let v_A,f be unknown (will be negative).
- Write momentum conservation:
  m_A v_A,i + m_B v_B,i = m_A v_A,f + m_B v_B,f.
- Compute initial momenta:
  m_A v_A,i = 6.5 × 13.6 = 88.4 kg·m/s.
  m_B v_B,i = 29.8 × (−17.8) = −530.44 kg·m/s.
  Total initial momentum = 88.4 − 530.44 = −442.04 kg·m/s.
- Compute B’s final momentum: m_B v_B,f = 29.8 × (−4.45) = −132.61 kg·m/s.
- Solve for v_A,f:
  −442.04 = 6.5 v_A,f + (−132.61)
  6.5 v_A,f = −442.04 + 132.61 = −309.43
  v_A,f = −309.43 / 6.5 = −47.605… m/s ≈ −47.60 m/s.

3) Why this answer is correct
- The calculation follows momentum conservation with correct sign convention and the stated final speed for B. The negative sign indicates West, so the final velocity of A is 47.60 m/s West.

4) Why the other choices are incorrect
- a (14.83 m/s W), c (68.01 m/s W), and d (10.38 m/s W) do not satisfy momentum conservation when substituted with the given masses and B’s final speed; only −47.60 m/s balances the total momentum.

Conclusion: The final velocity of trolley A is 47.60 m/s West, matching answer b.

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