Year: 2008
Paper: 1
Question Number: 10
Course: LFM Pure and Mechanics
Section: Constant Acceleration
No solution available for this problem.
There were significantly more candidates attempting this paper this year (an increase of nearly 25%), but many found it to be very difficult and only achieved low scores. The mean score was significantly lower than last year, although a similar number of candidates achieved very high marks. This may be, in part, due to the phenomenon of students in the Lower Sixth (Year 12) being entered for the examination before attempting papers II and III in the Upper Sixth. This is a questionable practice, as while students have enough technical knowledge to answer the STEP I questions at this stage, they often still lack the mathematical maturity to be able to apply their knowledge to these challenging problems. Again, a key difficulty experienced by most candidates was a lack of the algebraic skill required by the questions. At this level, the fluent, confident and correct handling of mathematical symbols (and numbers) is necessary and is expected; many students were simply unable to progress on some questions because they did not know how to handle the algebra. There were of course some excellent scripts, full of logical clarity and perceptive insight. It was also pleasing that one of the applied questions, question 13, attracted a very large number of attempts. However, the examiners were again left with the overall feeling that some candidates had not prepared themselves well for the examination. The use of past papers and other available resources to ensure adequate preparation is strongly recommended. A student's first exposure to STEP questions can be a daunting, demanding experience; it is a shame if that takes place during a public examination on which so much rides.
Difficulty Rating: 1500.0
Difficulty Comparisons: 0
Banger Rating: 1500.0
Banger Comparisons: 0
On the (flat) planet Zog, the acceleration due to gravity
is $g$ up to height $h$ above the surface and $g'$ at greater heights.
A particle is projected from the surface at speed $V$ and at an
angle $\alpha$ to the surface, where $V^2 \sin^2\alpha > 2 gh\,$.
Sketch, on the same axes, the trajectories in the cases $g'=g$
and $g' < g$.
Show that the particle lands a distance $d$ from the point of
projection given by
\[
d = \left(\frac {V-V'} g + \frac {V'}{ g'} \right)
V\sin2\alpha\,,
\]
where $V' = \sqrt{V^2-2gh\,\rm{cosec}^2\alpha\,}\,$.
This was the most popular mechanics question, and the question which gained the best marks across the entire paper. The sketch of the particle's trajectories in the two different scenarios was generally well done, with almost all candidates successfully completing the sketch. It was a little disappointing, though, that very few attempted to justify their assumption that the particle does, in fact, reach height h. The next stage, using the "suvat" equations to deduce d, was generally either done very well or very poorly. Of those who had difficulty, some were stuck trying to figure out how to go about the question, others were unsure of which of the "suvat" equations to use (despite all of the individual components of this question being very standard A-level problems), while some derived a quadratic equation (having used s = ut + ½at²) but were incapable of then solving it. Nonetheless, this question did require a sustained chain of logical steps, and it was pleasing to see over a quarter of the candidates who attempted this question gaining close to full marks on it.