A stationary firework explodes into three different fragments that move in a horizontal plane, as illustrated in Fig. 2.1. [Figure 2.1] The fragment of mass 3.0M has a velocity of 7.0ms⁻¹ perpendicular to line AB. The fragment of mass 2.0M has a velocity of 6.0 ms⁻¹ at angle θ to line AB. The fragment of mass 1.5M has a velocity of 8.0 ms⁻¹ at angle θ to line AB.

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

1. [M1] sum/total momentum (of a system of bodies) is constant OR sum/total momentum before = sum/total momentum after
2. [A1] for an isolated system or no (resultant) external force
3. [C1] (p =) mv or (3.0M × 7.0) or (2.0M × 6.0) or (1.5M × 8.0)
4. [C1] 3.0M × 7.0 = 2.0M × 6.0 sinθ + 1.5M × 8.0 sinθ
5. [A1] θ = 61°
6. OR (vector triangle method)
7. (C1) momentum vector triangle drawn
8. (A2) θ = 61° (2 marks for ±1°, 1 mark for ±2°)
9. OR (use of cosine rule)
10. (C1) p = mv or (3.0M × 7.0) or (2.0M × 6.0) or (1.5M × 8.0)
11. (C1) (21M)² = (12M)² + (12M)² – (2 × 12M × 12M × cos 2θ)
12. (A1) θ = 61°
13. [C1] (E =) ½mv²
14. [A1] ratio = (½ × 2.0M × 6.0²) / (½ × 1.5M × 8.0²) = 0.75