A-LevelMathematicsMechanics9709/42 · Feb/Mar 2019 · Q26 Marks
A particle is projected vertically upwards with speed 30 m s¯¹ from a point on horizontal ground.
- (i)Show that the maximum height above the ground reached by the particle is 45 m.[2]
- (ii)Find the time that it takes for the particle to reach a height of 33.75 m above the ground for the first time. Find also the speed of the particle at this time.[4]
Mark scheme
Marking points from the official mark scheme (Feb/Mar 2019). The mark or mark type is shown in brackets.
- [M1] Using v² = u² + 2as with v = 0, u = 30 and a = -g For any complete method for finding maximum height s
- [A1] AG s = maximum height = 900/20 = 45 m
- [M1] Applying s = ut + ½at² with s = 33.75, u = 30 and a = -g
- [M1] Solve a 3-term quadratic for t
- [A1] t = 1.5 (reject t = 4.5)
- [B1ft] Use v = u + at with u = 30 and t = 1.5 ft on t value found
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