A-LevelMathematicsMechanics9709/52 · May/June 2018 · Q47 Marks
A particle P is projected from a point O on horizontal ground with initial speed 20 m s⁻¹ and angle of projection 30°. At the instant t s after projection, the horizontal and vertically upwards displacements of P from O are x m and y m respectively.
- (i)Express x and y in terms of t and hence find the equation of the trajectory of P.[4]
- (ii)P is at the same height above the ground at two points which are a horizontal distance apart of 15 m. Calculate this height.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [B1] (i) x = (20cos30)t or 10√3 t
- [B1] (i) y = (20sin30)t - ½ gt² or 10t-5t²
- [M1] (i) y = (20sin30)[x/(20cos30)] – 5[x/(20cos30) ]²
- [A1] (i) y = x/√3 − x²/60 or 0.577x – 0.0167 x²
- [M1] (ii) x/√3 − x²/60 = (x+15)/√3 - (x+15)²/60
- [A1] (ii) x = 9.821
- [A1] (ii) y = 4.06(25) m
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