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22Oct2018

Leaving Certificate Examination 1953 Honours Applied Mathematics

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Question 1

The ends of a light inextensible string quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds feet long are attached to two pegs which are quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds feet apart and in the same horizontal line. A mass of quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds lb. is suspended from the string at a point which is quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds feet from one peg and quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds feet from the other. Find the tension in each part of the string.

Question 2

A block weighing quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds lb. can just rest without slipping on a rough plane when the plane is inclined at an angle of quicklatex.com-62849a846c4567532a083a01c484a779_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds to the horizontal. Find

(a) the magnitude of the least force in the horizontal direction,

(b) the magnitude and direction of the least force, that will keep the block from slipping when the plane is inclined at an angle of quicklatex.com-a39629676648ce22f385e71f73d8b697_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds to the horizontal.

Question 3

An engine weighing quicklatex.com-7260fe4f20eb47e11e44b79da133e21c_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds tons is pulling a train of weight quicklatex.com-88c065fecf0554f2316700e1f2bf361f_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds tons down an incline of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds in quicklatex.com-5291abebe16995c90201b72e133d15d8_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds. The speed of the train is quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds m.p.h. and it is accelerating at the rate of quicklatex.com-294859fdbb1fdda439ec2363e11fdfa1_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds ft. per secquicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds. If the frictional resistances to motion are equivalent to quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds lb. wt. per ton, find the horse-power at which the engine is working.

Question 4

A pile driver of mass quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds cwt. falls freely from rest through a distance of quicklatex.com-3883c8dfa7e1fd380cd2fa2674d982e2_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds feet and strikes a pile of mass quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds cwt. The pile driver and the pile move together as a single body after the impact and the pile is driven quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds inches into the ground. Find the average resistance of the ground, in tons weight.

Question 5

What is meant by the velocity of one body relative to another? Explain with the aid of a diagram how the velocity of quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds relative to quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds may be found if the velocities of quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds are known.

To a person on a ship travelling due East at quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds m.p.h., another ship two miles due South appears to be travelling at quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds m.p.h. in a direction quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds West of North. Find the velocity of the second ship in magnitude and direction.

What is the distance between the ships when they are nearest to each other?

Question 6

If quicklatex.com-63ab7de62920c09a3246a8ce084ab3ce_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds if the greatest height reached by a projectile, prove that

    quicklatex.com-1fe0913c90780a87ee5348362ed18c7c_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds

where quicklatex.com-ba05715987b9d18252648b0ecfc8eb72_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds is the initial velocity, quicklatex.com-0dce58ae1ea930bb9c39e85ab5e4c977_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds the angle of projection, and quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds the total time of flight.

Two vertical posts, each of height quicklatex.com-7e66f8d3fbb50779ceb68e5184deb32d_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds feet, stand quicklatex.com-f7fbd4b5770df1daffbe0cd1a0b8bdf9_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds feet apart on a horizontal plane. A particle is projected from a point on the plane at an angle of quicklatex.com-4a9ebc5b427b2b96f79ce7a73bb0b960_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds with the horizontal, and just clears the top of each post. If quicklatex.com-58834c2a51dceaf497b71827539019bd_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds is the greatest height reached by the particle, and v

    quicklatex.com-7906a3199f4e0c18b4599ba60e8ea583_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds

v^2=\frac{5}{2}gl

    quicklatex.com-fa1d0ce1835a2123a299818b9eb0c3fd_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds

x=a \sin \omega t – b \cos \omega t.

Show that the motion is Simple Harmonic, and find an expression for (i) the amplitude, (ii) the maximum velocity.

Find also an expression for the least time taken by the particle to travel a distance quicklatex.com-fc85ef309591bf8b549446f3ebd0b450_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds from its mean position.

Question 9

A triangular lamina quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds is immersed in a vertical position in water with its vertex quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds at the surface and its base quicklatex.com-3675ba693016b80ac93fbf734e15678b_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds parallel to the surface. The base is quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds inches in length, and the height of the triangle is quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds inches. Find the total thrust of the water on quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds.

quicklatex.com-05d30bc5e19b413cea824383c6bce148_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds, quicklatex.com-c8abc5e5c1ec96e74c27c739f796cedb_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds are two points on quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds, quicklatex.com-371fe833e9a89e2790fc66adb618b944_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds respectively such that the straight line quicklatex.com-cacf86ec54fe47688ea7a15a4ca0d7d0_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds is horizontal. If the thrust on quicklatex.com-759670c01a244f735571a4913a873980_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds is one-eight of the thrust on quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds, find the depth of quicklatex.com-cacf86ec54fe47688ea7a15a4ca0d7d0_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds below the surface.

[One cubic foot of water weight quicklatex.com-2a62b4fd8e04c54613a6683d3f1636ef_l3 | Leaving Certificate Examination 1953 Honours Applied Mathematics | Maths Grinds lb.]

 


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:

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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.

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

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

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