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22Nov2018

Leaving Certificate Examination 1962 Honours Applied Mathematics

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Question 1

A uniform ladder is put leaning against a rough vertical wall (coefficient of friction quicklatex.com-9a61841f2abe3e6f5e5b707bbfade7f4_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds), the bottom of the ladder being on a rough horizontal plane (coefficient of friction quicklatex.com-d87274adcc3e9b397c1d81918125c810_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds). What is the least angle the ladder can make with the plane without slipping?

Question 2

quicklatex.com-0bc2407dfe67fc49000363238a97afd0_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds is quadrilateral lamina in which quicklatex.com-cde3e80c0b1bc8cff602c5c6fb7f1466_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds, quicklatex.com-2bc8b92466fb8df4de567451d7b7b774_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds, quicklatex.com-0b015e3dc77f8516e1e985f366a6b858_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds and quicklatex.com-a3654a8d1bdc3254aa7a37dc1ec08c68_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds. Find the position of its centre of gravity.

Question 3

(i) quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds is travelling due west at quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds m.p.h. and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds is travelling at quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds m.p.h. in a direction quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds west of south. Find the velocity of quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds relative to quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds, in magnitude and direction.

(ii) A steady wind blowing at quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds m.p.h. To a man walking due east quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds m.p.h. the wind appears to be blowing from the north-east. Find the actual direction of the wind.

Question 4

If a projectile takes a time quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds to travel between two points which are in the same horizontal line, show that the greatest height if reaches above that line is quicklatex.com-36d6f791e337ded029e8d0b32b497bd5_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds.

Two vertical posts of equal height stand quicklatex.com-31b32a58a89a79009fa2eb15af8bf5af_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds feet apart on a horizontal plane. A particle is projected from a point in the plane quicklatex.com-e0a499662d95f1ba018ae5f8750be1ed_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds feet from the nearer post and just clears the top of each post. If the greatest height the particle reaches is quicklatex.com-3883c8dfa7e1fd380cd2fa2674d982e2_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds feet higher than the tops of the posts, find its initial velocity.

Question 5

A car of mass one ton, descending an incline of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds in quicklatex.com-5291abebe16995c90201b72e133d15d8_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds, accelerated uniformly from quicklatex.com-8a0f60b8ca3ec09a3984d53508863c9a_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds m.p.h. to quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds m.p.h. in quicklatex.com-72ca69268f6920f4a19021893b9df033_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds yards. Find the acceleration in ft. per secquicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds.

If the frictional resistances to motion were equivalent to quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds lb. wt., find the horse-power at which the car was working when its speed was quicklatex.com-66bafba23129fa8ab0a7d7fd2fc25d52_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds m.p.h.

Question 6

A bullet of mass quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds ounces is first with a velocity of quicklatex.com-273bc6cb499f0769af809745ecec0361_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds ft. per. sec. from a gun of mass quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds lb. which is free recoil. Find the velocity with which the gun begins recoil, and find the total kinetic energy of the bullet and the gun in foot-pounds.

If the bullet had been fired with the same velocity from another gun, the total kinetic energy would have been greater by quicklatex.com-287a55b2d8cfd44f5f1f05ad3a5a70db_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds foot-pounds. Find the mass of the other gun.

Question 7

A body of mass quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds lb. suspended from a fixed peg by a light inextensible string quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds feet long is describing a horizontal circle at a uniform rate of quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds radians per second. Find the tension in the string, in lb.wt., and find the angle which the string makes with the vertical.

What vertical distance would the body rise if its angular velocity were increased to quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds radians per second?

Question 8

A particle is moving along a straight line so that is distance quicklatex.com-ada3765a264ac03a253ee0ccbe61f602_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds(cm.) from a fixed point quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds at time quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds(sec.) is given by the formula quicklatex.com-592a26e9e7263b5895c8feaaf937a947_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds. Show that the motion is simple harmonic.

Find (i) the period of the motion, (ii) the distance the particle travels from quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds in a quarter of a second, (iii) the time the particle takes to travel quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds feet from quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds, (iv) the velocity of the particle when its acceleration is half its maximum acceleration.

Question 9

quicklatex.com-0bc2407dfe67fc49000363238a97afd0_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds is a quadrilateral lamina in which quicklatex.com-4177878327c98c954558813f6aa4e052_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds cm., quicklatex.com-802b359a2e897446a616367c83ef30a5_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds cm. and quicklatex.com-6a2bef378deee9ec3582ebc059370a6d_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds cm. The lamina is immersed in water with the vertex quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds  vertically below quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds. Find the total thrust of the water on the lamina

(i) when quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds is at the surface,

(ii) when quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds is quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds cm. below the surface,

(iii) when quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds is quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1962 Honours Applied Mathematics | Maths Grinds cm. above the surface.

(A cubic centimetre of water weighs one gram.)


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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