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29 Nov 2018

Leaving Certificate Examination 1969 Honours Applied Mathematics

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Question 1

State the principle of the conservation of momentum.

A car weighing quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds tons and moving at quicklatex.com-5710ac6ade182d0ad850e6efd2e4a189_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds m.p.h. along a main road collides with a lorry of weight quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds tons which emerges at quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds m.p.h. from a crossroad at right angles to the main road. If the two vehicles lock, what will be their velocity after the collision?

Question 2

A helicopter flies from an aerodrome to a place due North, a distance quicklatex.com-b2de1827bec6a60693b2ac81778d5023_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds kilometers from the aerodrome, and then returns. The speed of the helicopter in still air is quicklatex.com-4b0d4dcf22295c195c00f05d04a405f7_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds meters/sec. and there is a wind of speed quicklatex.com-c2d13186921994c33eb382dd54c357b9_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds meters/sec. blowing from the North-East throughout the journey. Show that the actual speed of the helicopter on the outward journey is quicklatex.com-24746e8a1a6c5c694c7889aa45349e68_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds meters/sec. and calculate the total time for both journeys.

Question 3

(i) Two identical uniform rods quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds and quicklatex.com-3675ba693016b80ac93fbf734e15678b_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds are rigidly connected at right angles at quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds. Find the centre of gravity of the compound body. The body is freely suspended from quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds. Find the inclination of quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds to the vertical.

(ii) A thin uniform wire is bent into the shape of a quadrilateral quicklatex.com-e0fa8e17620a5116a336a68e895abd4f_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds. The coordinates of the vertices are quicklatex.com-b5a1da2b8b79b9f6cb919cfef36d68f5_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds, quicklatex.com-1cdbae3ebee672eeebde23df0815cbf9_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds, quicklatex.com-da3236096b60cb1405ff4e6cd39cacd9_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds and quicklatex.com-f6edba9754e874ef1da1969aa8a4bb80_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds. Find the coordinates of the centre of gravity of the wire.

Question 4

A projectile is fired with an initial speed of quicklatex.com-4c8846d90c9db2c7945bc56cc2df5c3f_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds ft./sec. to hit a target at a horizontal distance of quicklatex.com-3883c8dfa7e1fd380cd2fa2674d982e2_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds ft. from the point of projection and at a vertical height of quicklatex.com-d61119651ddf565da4198bb11ee60847_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds ft. Find the two possible angles of projection and the ratio of the times of flight along the two paths. Find the speed of the projectile at impact in each case.

(Take quicklatex.com-32a1fff034751d4fc3e4edc15ca376af_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds to be quicklatex.com-094ee6d517670326a569d5b0dc00b494_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds ft./secquicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds.).

Question 5

A train of mass quicklatex.com-4fbb80c3d7c3c9bdfaf780287e19f597_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds tons and of constant quicklatex.com-5bdaee7a8dcd622a3a917f6a17e7e80d_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds horse-power, is allowed to run with the engine turned off down a slope of inclination quicklatex.com-d85f3b0b8f21707463f12d110f916f98_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds to the horizontal and reaches a maximum speed of quicklatex.com-5291abebe16995c90201b72e133d15d8_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds m.p.h. Find the resistance to motion in tons weight. If the resistance to motion in all cases is directly proportional to the square of the speed, calculate the acceleration of the train on a level track when its speed is quicklatex.com-5710ac6ade182d0ad850e6efd2e4a189_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds m.p.h.

(Take quicklatex.com-32a1fff034751d4fc3e4edc15ca376af_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds to be quicklatex.com-094ee6d517670326a569d5b0dc00b494_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds ft./secquicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds.).

Question 6

A car quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds moves along a straight road quicklatex.com-e979ae05a61debd12da167a83e2720d6_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds with constant acceleration of quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds ft/secquicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds. in the direction quicklatex.com-e979ae05a61debd12da167a83e2720d6_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds its velocity at quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds is quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds ft/sec. in the same direction. Three seconds after quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds has left quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds another car quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds starts from quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds with a velocity of quicklatex.com-95780ea18fb27786ad9c02969c565bba_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds ft/sec. and a uniform acceleration of quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds ft/secquicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds., both in the direction quicklatex.com-e979ae05a61debd12da167a83e2720d6_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds. When and where will quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds overtake quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds? Show that after passing quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds, quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds will never be ahead by more that quicklatex.com-094ee6d517670326a569d5b0dc00b494_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds ft.

Question 7

A particle of mass quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds lbs. is suspended from a fixed point quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds by a light inelastic string of length quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds feet. It is projected horizontally with speed quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds ft./sec. from a point quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds feet vertically below quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds. How high does it rise in the subsequent motion?

When it returns to quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds it collides and coalesces with a stationary particle of mass quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds lbs. How high does the combined mass rise in the subsequent motion?

Calculate the greatest tension in the string during the motion of the combined mass.

(Take quicklatex.com-32a1fff034751d4fc3e4edc15ca376af_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds to be quicklatex.com-094ee6d517670326a569d5b0dc00b494_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds ft./secquicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds.).

Question 8

Define simple harmonic motion.

A particle is moving in a straight line with simple harmonic motion. When it is quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds feet from the centre of its path its speed is quicklatex.com-4c8846d90c9db2c7945bc56cc2df5c3f_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds ft./sec. and when it is quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds feet away its speed is quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds ft./sec. Find the period and amplitude of the motion. Find also the time taken for the particle to travel from the centre of its path to a point where its speed is half the maximum speed.

Question 9

Two solid uniform spheres each of radius quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds cms. are connected by a light string and are completely immersed in a tank of water. The specific gravitates of the spheres are quicklatex.com-294859fdbb1fdda439ec2363e11fdfa1_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds and quicklatex.com-c20f4cdda6f8d62e84bdeecce0a65eb8_l3 | Leaving Certificate Examination 1969 Honours Applied Mathematics | Maths Grinds respectively. Find the tension in the string and the reaction between the bottom of the tank and heavier sphere.


Citation:

State Examinations Commission (2018). State Examination Commission. Accessed at: https://www.examinations.ie/?l=en&mc=au&sc=ru

Malone, D and Murray, H. (2016). Archive of Maths State Exams Papers. Accessed at: http://archive.maths.nuim.ie/staff/dmalone/StateExamPapers/

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The EU Directive 2003/98/EC on the re-use of public sector information, its amendment EU Directive 2013/37/EC, its transposed Irish Statutory Instruments S.I. No. 279/2005, S.I No. 103/2008, and S.I. No. 525/2015, and related Circulars issued by the Department of Finance (Circular 32/05), and Department of Public Expenditure and Reform (Circular 16/15 and Circular 12/16).

Note. Circular 12/2016: Licence for Re-Use of Public Sector Information adopts CC-BY as the standard PSI licence, and notes that the open standard licence identified in this Circular supersedes PSI General Licence No: 2005/08/01.

Links:

https://circulars.gov.ie/pdf/circular/per/2016/12.pdf

https://creativecommons.org/licenses/by/4.0/legalcod

 

 

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