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GCE JUN 2009 : AS, M2: Mechanics 2

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ADVANCED General Certificate of Education 2009 Mathematics assessing Module M2: Mechanics 2 AMM21 AMM21 Assessment Unit M2 [AMM21] THURSDAY 11 JUNE, MORNING TIME 1 hour 30 minutes. INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number on the Answer Booklet provided. Answer all seven questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. You are permitted to use a graphic or a scientific calculator in this paper. INFORMATION FOR CANDIDATES The total mark for this paper is 75 Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question. Answers should include diagrams where appropriate and marks may be awarded for them. Take g = 9.8 m s 2, unless specified otherwise. A copy of the Mathematical Formulae and Tables booklet is provided. Throughout the paper the logarithmic notation used is ln z where it is noted that ln z loge z 4299 Answer all seven questions. Show clearly the full development of your answers. Answer should be given to three significant figures unless otherwise stated. 1 A particle of mass 5 kg is acted on by three forces F1, F2 and F3 newtons, where F1 = 4i + 2j + k F2 = 5i + 2j + 2k F3 = pi + qj 3k The particle is moving with acceleration (i + j) m s 2 (i) Find p and q. [7] When the particle is at the origin O, it has an initial velocity of (i + 2k) m s 1 (ii) Find its velocity after 3 seconds. (iii) Find its displacement from O after 6 seconds. 2 [3] [3] Fig. 1 below shows a skier of mass 80 kg subject to a resistance, R, as he descends a slope. He starts from rest at a point, A, 800 m above sea level and skis to the bottom of the slope, B, which is 500 m above sea level. His velocity at B is 15 m s 1 A 800 m 500 m B Fig. 1 (i) Find the increase in the kinetic energy of the skier. (ii) Find the work done by gravity. [2] (iii) Hence, using the Work Energy Principle, find the work done by R. [5] (iv) State one modelling assumption you have made in answering this question. 4299 [3] [1] 2 [Turn over 3 At time t seconds, a particle has velocity v m s 1 given by v = 3ti 3tj + 3k (i) Find the speed of the particle when t = 2 [3] At t = 0 the particle has displacement (i + 3j) metres relative to an origin O. (ii) Find the displacement of the particle from O at time t = 4 4 [5] Ann and her bicycle have a total mass of 60 kg. She cycles at a constant speed of 8 m s 1 along a straight horizontal road against a resisting force S newtons. Ann works at a constant rate of 500 W. (i) Find S. [4] Ann now ascends a hill inclined at sin 1 1 to the horizontal. 7 She continues to work at 500 W and the resisting force remains the same. (ii) Find her acceleration when she is ascending the hill with a speed of 2 m s 1 4299 3 [6] [Turn over 5 Fig. 2 below shows two particles P and Q attached by a light inextensible string. The string passes through a smooth hole, O, in a smooth horizontal surface. Q, mass 5 kg, hangs vertically below O and remains at rest. P, mass 2 kg, moves in horizontal circles, centre O, on the surface. P O Q Fig. 2 (i) Draw a diagram showing all the external forces acting on P and Q. [2] (ii) Find the tension in the string. [2] P moves with angular speed 10 rad s 1 (iii) Find the radius of the circle. 6 [5] An ice puck of mass 0.2 kg has an initial speed of 25 m s 1 along an icy horizontal surface. During its time of motion, a horizontal resistance of magnitude 0.005v2 N acts to oppose its motion. At time t seconds, the puck moves with velocity v m s 1 Model the puck as a particle. (i) Show that the equation of motion of the particle can be modelled by dv = 0.025v2 dt (ii) Find the speed of the puck when t = 2 4299 [3] [8] 4 [Turn over 7 A particle is projected from a point O on horizontal ground with a speed of u m s 1 and at an angle above the horizontal, as shown in Fig. 3 below. P u y O x Fig. 3 After t seconds, the particle passes through a point P. P is x metres horizontally and y metres vertically from O. (i) Show that the time taken for the particle to reach P is x t = u cos [3] (ii) Hence, show that the particle follows a path whose equation is gx2 y = x tan 2u2 cos2 [4] The crossbar of a set of rugby posts on a horizontal pitch is 2.5 m above the ground. A kicker kicks a ball from a point O with a speed of u m s 1 and at an angle of 30 above the horizontal. The ball just clears the crossbar. The horizontal component of the distance travelled by the ball until it clears the crossbar is 50 m. Model the ball as a particle. (iii) Find u (iv) Find the maximum height reached by the ball. 4299 [3] [3] 5 [Turn over 938-015-1 8 [Turn over

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Additional Info : Gce Mathematics June 2009 Assessment UnitM2 Module M2 : Mechanics 2
Tags : General Certificate of Education, A Level and AS Level, uk, council for the curriculum examinations and assessment, gce exam papers, gce a level and as level exam papers , gce past questions and answer, gce past question papers, ccea gce past papers, gce ccea past papers

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