A particle P of mass 0.2kg is projected vertically upwards from horizontal ground with speed 25ms⁻¹.

Mark scheme

Marking points from the official mark scheme (May/June 2024). The mark or mark type is shown in brackets.

1. [M1] For use of v² = u² + 2as or equivalent to get an equation in v only with u = 25, s = 20 and a = ±g.
2. [A1] AG Allow verification – at least one intermediate step from equation of motion to given result. Any errors seen is A0.
3. (M1) Attempt at energy with m = 0.2, h = 20, u = 25; correct number of terms, allow sign errors.
4. (A1) AG Allow verification - at least one intermediate step from conservation of energy to given result. Any errors seen is A0.
5. [M1] OE Attempt at conservation of momentum; 3 non-zero terms; allow sign errors – use of 25 is M0.
6. [A1] Must have direction (possibly seen on diagram). If using mgv for momentum, then M1 A0 max.
7. [B1] From v² = 0 + 2 × g × 20 (OE) - possibly implied by speed of P after impact being stated at 10.
8. [B1] From 20 = 0 + (1/2) × g × t² (OE).
9. [M1] Distance travelled by P after impact with the ground. Must be using their 10 (speed of P after impact with the ground) and a = ±g.
10. [M1] Distance travelled by Q after P's impact with the ground. Must be using their ±10 (the speed/vel. of Q after their 2 s (=|'10'+(-g)×2| where ‘10' is the value from (b)) and a = ±g.
11. [A1] Time after P hits the ground to next collision.
12. [A1] CWO
13. (M1) Expression for the displacement of Q after first impact of P and Q. Must be using their 10 (from (b)) and a = ±g.
14. (M1) Expression for the displacement of P (for values of t≥ 2) measured from point of first collision between P and Q. Must be using their 2 (time for P to reach ground), their 10 (speed of P after impact with the ground), a = ±g.
15. (A1) Correct time between collisions of P and Q.
16. (A1) CWO