A-LevelMathematicsMechanics9709/42 · Oct/Nov 2017 · Q46 Marks
A particle P is projected vertically upwards from horizontal ground with speed 12 m s⁻¹.
- (i)Find the time taken for P to return to the ground.[2]
- (ii)The time in seconds after P is projected is denoted by t. When t = 1, a second particle Q is projected vertically upwards with speed 10 m s⁻¹ from a point which is 5 m above the ground. Particles P and Q move in different vertical lines. Find the set of values of t for which the two particles are moving in the same direction.[4]
Mark scheme
Marking points from the official mark scheme (Oct/Nov 2017). The mark or mark type is shown in brackets.
- [M1] [12t - ½gt² = 0] or [0 = 12 - gT] with t = 2T used Using s = ut + ½at² or equivalent such as finding time T to highest point and doubling.
- [A1] t = 2.4 s
- [B1] Critical point at t = 1.2 Seen in 4(ii)
- [B1] Critical point at t = 2 Seen in 4(ii)
- [B1] Both moving in same direction 1 < t < 1.2
- [B1] Both moving in same direction 2 < t < 2.4
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