Two particles, P and Q, of masses 2mkg and mkg respectively, are held at rest in the same vertical line. The heights of P and Q above horizontal ground are 1 m and 2m respectively. P is projected vertically upwards with speed 2 ms⁻¹. At the same instant, Q is released from rest.

Mark scheme

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

1. [M1] For use of s = ut + 1/2 at² at least once with a = ±g and u=0 or u=±2. Seen anywhere.
2. [M1] Use s_P + s_Q = ±(2-1) OR ±1 ONLY with s_P and s_Q of the correct form
3. [A1] Must be positive.
4. [A1] Must be positive. If A0A0, allow SCB1 if both are negative
5. [*M1] Use of conservation of momentum; 4 non-zero terms; using their±3 ms⁻¹ and their±5 ms⁻¹; allow sign errors and m missing ONLY. Do not allow with v_P = ±2 or with v_Q = 0. Do not allow made up values for 3 and 5. Allow LHS of our equation to have only one term but only if getting v_P = 0 in (a) from s_P = s_Q.
6. [A1] Allow v = -3.75 from correct work.
7. [*B1] This may be seen in part (a), but do not award the mark until stated/used in part (b).
8. [DM1] Use of v²=u² +2as using their v and a=±g; their s is either [1+(1/4)] or [2-(5/4)] OE.
9. [A1] Or √465/4; AWRT 5.39; 5.390964...