A-LevelMathematicsMechanics9709/51 · May/June 2018 · Q49 Marks
A small object is projected from a point O with speed V m s¯¹ at an angle of 45° above the horizontal. At time t s after projection, the horizontal and vertically upwards displacements of the object 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 path.[4]
- (ii)The object passes through the point with coordinates (24, 18). Find V.[2]
- (iii)The object passes through two points which are 22.5 m above the level of O. Find the values of x for these points.[3]
Mark scheme
Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.
- [B1] x = (Vcos45)t; Use horizontal motion
- [B1] y = (Vsin45)t – gt²/2; Use s = ut + ½gt² vertically
- [M1] y = (Vsin45)x / (Vcos45) – ½g(x / (Vcos45))²; Attempt to eliminate t
- [A1] y = x – 10x² / V²
- [M1] 18 = 24 – 10 × 24² / V²; Substitutes x = 24, y = 18 in part (i) equation
- [A1] V = 31(.0)
- [M1] 22.5 = x – 10x² / 960; Put y = 22.5 in part (i)
- [M1] x² - 96x + 2160 = 0; Attempt to solve a quadratic equation
- [A1] x = 36, 60
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