A particle P of mass 0.4 kg is projected vertically upwards from horizontal ground with speed 10ms-1.

Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

1. [M1] For use of v² = u² + 2as with v = 0, u = ±10 and a=±g or ±10 and solve for s (or any other complete SUVAT method). Or using an energy method: 0.4gh = ¹/₂(0.4)(10)² and solve for h (with two terms using correct given values – condone lack of masses in conservation of energy equation).
2. [A1]
3. [B1FT] Or loss of PE = ± 0.4 × g × 5 using their maximum height from (a).
4. [*M1] M1 for ¹/₂×0.4v² = KE/PE before impact – 7.2 (must be correct method of subtracting 7.2 (OE)). Or, for finding the maximum height after first impact. Need not solve for v (or h) for this mark.
5. [DM1] For use of a complete method to find t. Condone sign errors but a = ±g. If calculating the time to the maximum height between the first and second impacts, then candidates must double this answer (OE). E.g., 0=8+(-g)T, t = 2T = ... or 3.2 = 0-0.5x-gxT² ⇒ t = 2T = ....
6. [A1]