A particle P is projected vertically upwards with speed 25 m s⁻¹ from a point 3 m above horizontal ground.

Mark scheme

Marking points from the official mark scheme (May/June 2019). The mark or mark type is shown in brackets.

1. [M1] Use of v = u + at with u = 25, v = 0 and a = -g or other complete method for finding t to highest point
2. [A1] t = 2.5
3. [M1] Applying s = ut + ½at² with s = 20, u = 25
4. [M1] Solve a 3-term quadratic for t, factorising or formula
5. [A1] Required time = 4 – 1 = 3 seconds
6. Alternative method for question 2(ii)
7. [M1] Using v² = u² + 2as with u = 25, s = 20 and a = -g
8. [M1] Use v at s = 20 to find the time, T, taken to reach the maximum height and to return to s = 20
9. [A1] Required time = 1.5 + 1.5 = 3 seconds
10. [M1] Using their t from 2(i) – 0.5 in s = ut + ½at² Allow finding h without taking note of the additional 3 m
11. [A1] h = 33 m
12. Alternative method for question 2(iii)
13. [M1] For attempting to find both the maximum height and the distance fallen in 0.5 seconds
14. [A1] h = 31.25 – 1.25 + 3 = 33 m