My Journal

All things Mathematical
2Oct2018

Leaving Certificate Examination 1945 Honours Applied Mathematics

/
Posted By
/
Comments0
Question 1

The velocities of two points quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds being known in magnitude and direction, explain with the aid of a diagram how to find the velocity of quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds relative to quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds.

A ship quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds sailing north at quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds miles per hour observes a ship quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds miles to the north-east which is sailing west at the rate of quicklatex.com-3c4de7b9ce82b47f9788dc2416e4c750_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds miles per hour. Calculate when they will be nearest to each other.

Question 2

quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds and quicklatex.com-3675ba693016b80ac93fbf734e15678b_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds are equal uniform bars, each of weight quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds lb., freely hinged at quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds ; and quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds and quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds are connected by a light cord such that the angle quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds is quicklatex.com-8a31becb362adc52e8f92b8a182effad_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds. quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds stands in a vertical plane with quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds and quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds on a smooth horizontal tale and a body of weight quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds lb. is suspended from a point quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds in quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds such that quicklatex.com-c299c8d3d5e15bbeb3e6e998a41e4cfa_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds. Find (i) the reactions of the table at quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds and at quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds and (ii) the tension in the cord.

Question 3

State the laws of friction.

Calculate to the nearest pound the least horizontal force which would push a mass of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds ton up an inclined plane of inclination quicklatex.com-7ba179480c0aba9b14c9e68eb8be20ca_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds, the coefficient of friction being quicklatex.com-722eef029ecdcc270d6177f20f496db1_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds.

Question 4

A cubical box, with lid, is made of uniform thin metal. The lid can turn on hinges of negligible weight along one edge of the top of the box and is fixed in position after having been opened through an angle of quicklatex.com-9c3fb28be0c20ddb0b2c4bd59c303de8_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds.

If the length of the edge of the box is 18″ find the distances of teh c.g. from the base of the box and from the vertical plane through the hinges.

If the box is placed on a plane which is slowly tilted about a line which is parallel to the line of the hinges, the latter being at a lower level than the parallel edge at the top of the box, find the inclination of the plane when the box is about to topple. [The plane is assumed to be rough enough to prevent sliding.]

Question 5

How far must a ram weighing quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds cwt. fall freely to drive a pile weighing quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds cwt. quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds inches into the ground against a total average resistance of quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds tons, assuming that the ram moves on with the pile.

Question 6

The bob of a simple pendulum of length quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds feet is projected horizontally from the position of equilibrium with a velocity of quicklatex.com-c30623542a0c9b8b7e1d25e72101c539_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds ft. per second so that after projection it begins to move in a vertical circle. Find (i) the vertical height of the bob above the point of projection when the string becomes slack and (ii) the greatest height attained by the bob.

Question 7

An engine working at quicklatex.com-756d205977874d6e3a71918445be01f5_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds horse-power pulls a train of quicklatex.com-0a7d1908dc17ba7c399644cfaecdaeba_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds tons (including the weight of the engine) along a level track, the resistances being quicklatex.com-3c4de7b9ce82b47f9788dc2416e4c750_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds lb. per ton. When the velocity is quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds miles per hour find its acceleration.

At what steady speed will the engine pull the train up an incline of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds in quicklatex.com-4fbb80c3d7c3c9bdfaf780287e19f597_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds with the same expenditure of power against the same resistances?

Question 8

A load of quicklatex.com-054ef36c6e54f65ccdd586c0869b4fb0_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds lb. is raised from rest by means of a rope the tension in which is quicklatex.com-37847b73f4b652eacdfa58601a02fe6f_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds. At a certain point the tension ceases so that the load comes to rest quicklatex.com-63ab7de62920c09a3246a8ce084ab3ce_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds feet above its initial position. Show that the time take is

    quicklatex.com-4d9a1f691986de5272c7144adfe012ef_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds

.

Question 9

Prove that if the acceleration in simple harmonic motion of amplitude quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds is quicklatex.com-a2e2324fb7c6de1277d5a656bc61e9ec_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds, where quicklatex.com-ada3765a264ac03a253ee0ccbe61f602_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds is the displacement from the mean position, the velocity is quicklatex.com-a2dc8aaa49d3619262d00dc7e814f9d4_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds.

A body moving in a straight line with simple harmonic motion has a velocity of quicklatex.com-edeca52e97715225ceecec173423f15e_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds ft. per sec. at a distance of quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds feet from its mean position and its greatest velocity is quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1945 Honours Applied Mathematics | Maths Grinds ft. per sec. Find the periodic time and amplitude.

 


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

print

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.