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16 Oct 2018

Leaving Certificate Examination 1949 Honours Applied Mathematics

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Question 1

quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds is a triangle in which quicklatex.com-12708d2c7ad3b9bc1c495b41ae6ade51_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds cm., quicklatex.com-78a3020f75ec3adfa84767d15661c817_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds cm., and quicklatex.com-448c315e05040b7e41cc3322ff1c5cd0_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds cm. Forces of quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds, quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds, quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds lb. wt. act along the sides quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds, quicklatex.com-c703974f82fa531d93879bbfbfb6c9cb_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds, quicklatex.com-156c32c8826a40241f75e66f5f0ad483_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds, respectively. Find the magnitude of their resultant and find how far from quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds it cuts quicklatex.com-c703974f82fa531d93879bbfbfb6c9cb_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds and the angle it makes with quicklatex.com-c703974f82fa531d93879bbfbfb6c9cb_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds.

Question 2

(a) Three coplanar forces quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds, quicklatex.com-6ce7c226153d55058c10348c6739a4c5_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds, quicklatex.com-b90475b22ab5c52e8edfa41828a34159_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds act along the straight lines quicklatex.com-10d7b3f9c2cfee3c3af0d6b6e9a1886f_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds, quicklatex.com-883c66734b6c9076472fde380fcb458b_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds, quicklatex.com-5b88d34f225f181402d7d742d3a51e8c_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds, respectively, and are in equilibrium. Prove that quicklatex.com-242f769685b8e4eecc24505777ddbf06_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds.

(b) The ends of a light string are attached to two points quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds, quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds respectively in the same horizontal line. A quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds lb. wt. and a body of unknown weight are suspended from the string at two points quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds, quicklatex.com-e24826b0fac28861acd034428af346f0_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds respectively. In the position of equilibrium the angles quicklatex.com-fb066c2e6d9648b8feaea8e556ecf822_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds, quicklatex.com-85f9dcfd39c064eb168216b9ecf6a3a0_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds, quicklatex.com-04a089f3fc02f11a381ad4a348c16e2e_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds are found to be quicklatex.com-43254279a766115b4c8c77b4f9e086ff_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds, quicklatex.com-08bd7dd7d66bdf57cea2741a7e8d1788_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds, quicklatex.com-a167991e6500d652c6496c53e44145a7_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds, respectively. Calculate the weight of the body.

Question 3

A cylindrical glass jar of internal diameter quicklatex.com-edeca52e97715225ceecec173423f15e_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds cm. and internal depth quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds cm. weights quicklatex.com-756d205977874d6e3a71918445be01f5_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds gm. and is open at the top. The bottom is quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds cm. thick and its weight is one-half of that of the whole jar. Find the depth of the centre of gravity from the top when the jar contains water to a depth of quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds cm.

[quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds c.c. of water weighs quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds gm.]

Question 4

A quicklatex.com-edeca52e97715225ceecec173423f15e_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds ounce mass is projected vertically upwards with an initial velocity of quicklatex.com-e2421346fe4da17e1d74a7cb53af7968_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds ft./sec. and quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds seconds later a quicklatex.com-fef30ec83d548cacaa4710d12bb69dc3_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds ounce mass is projected vertically upwards from the same place and with the same initial velocity. Assuming that the masses coalesce when they collide, find the total time that elapses before the combined mass returns to the point of projection. What kinetic energy is lost by the collision?

Question 5

A circular racing-track of quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds laps to the mile is banked at an angle of quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds to the horizontal. At what speed on the track will a cyclist have no tendency to skid?

If the coefficient of friction is quicklatex.com-cb886097882c605a2c3c9215e6cdf120_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds, what is the greatest speed at which a cyclist could travel on the track without skidding?

Question 6

A particle is projected at an angle of quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds to the horizontal with a velocity of quicklatex.com-4fbb80c3d7c3c9bdfaf780287e19f597_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds ft./sec. from the top of a tower quicklatex.com-15ac81bac6abf9dbbed52f24900160ae_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds feet high. Find at what horizontal distance from the foot of the tower it will strike the ground and its velocity, in magnitude and direction, when it reaches the ground.

Question 7

A train of mass quicklatex.com-fef5d9bb0bd664dfe03d2ae1a00c063d_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds tons is travelling at a uniform speed of quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds miles per hour on a horizontal track. Half a mile from a station a coach of mass quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds tons is slipped and the rest of the train proceeds under the same tractive force as before. If the resistance to motion is always quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds lb. wt. per tone, find (a) the H.P. at which the engine is working, (b) the uniform force with which the coach must be braked after it is slipped so that it may come to rest at station, (c) the distance the train is past the station when the coach arrives.

Question 8

A particle starts from rest and moves with simple harmonic motion. Its velocity after covering a distance of quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds feet from rest is quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds ft./sec. and its maximum velocity is quicklatex.com-c20f4cdda6f8d62e84bdeecce0a65eb8_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds ft/sec. Find its maximum acceleration and the periodic time.

Question 9

A rectangular trough with vertical sides and a square base of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds ft. edge is filled with mercury (sp. gr. quicklatex.com-b4a3222b53a62e3f2494ccd3d0875c9f_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds) to a depth of quicklatex.com-3883c8dfa7e1fd380cd2fa2674d982e2_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds inches. Find the total thrust on the base and the total thrust on a vertical side.

If water to a depth of quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds inches is poured on top of the mercury, find the increase in the total thrust on a vertical side.

[quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds c. ft. water weights quicklatex.com-287a55b2d8cfd44f5f1f05ad3a5a70db_l3 | Leaving Certificate Examination 1949 Honours Applied Mathematics | Maths Grinds lbs.]

 


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/

Licence:

“Contains Irish Public Sector Information licensed under a Creative Commons Attribution 4.0 International (CC BY 4.0) licence”.

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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