A particle P is projected from a point O with speed V ms¯¹. At time t s after projection the horizontal and vertically upwards displacements of P from O are x m and y m respectively. The equation of the trajectory of P is y = 2x - (25x² / V²).

Mark scheme

Marking points from the official mark scheme (May/June 2017). The mark or mark type is shown in brackets.

1. [B1] Note θ = 63.4349..° tan θ = 2
2. [B1] Substitutes x = y = a into the trajectory equation a = 2a – 25 a² / V² (25a = V²)
3. [B1] Horizontal motion a = Vcos63.4349.. × 4
4. [M1] Attempts to eliminate a V² = 25 × 4 × Vcos63.4349..
5. [A1] V = 44.7(213..) or 20√5
6. [A1] a = 80
7. [B1] Uses s = ut + at² / 2 t2/2 vertically a = Vsin63.4349..× 4 – g4²/2
8. [B1] Horizontal motion a = Vcos63.4349..× 4
9. [M1] Attempts to solve the 2 equations Vsin63.4349..× 4 – g4² / 2 = Vcos63.4349..× 4
10. [A1] V = 44.7(213..)or 20 √5
11. [A1] a = 80
12. [M1] v_y = vertical component of the velocity
13. [M1] tanα = v_y/v_x where v_x = horizontal velocity
14. [A1] α = 0°