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28 Nov 2018

Leaving Certificate Examination 1968 Honours Applied Mathematics

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Question 1

Show how to find the centre of gravity of a non-rectangular parallelogram.

A thin uniform square sheet of metal quicklatex.com-0bc2407dfe67fc49000363238a97afd0_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds of area quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds square inches weighs quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds ounces. At the corners quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds, quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds, quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds, quicklatex.com-e24826b0fac28861acd034428af346f0_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds weights of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds oz., quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds oz., quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds oz., and quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds oz., respectively are placed. Locate the centre of gravity of the system.

Question 2

 

Establish the formulae quicklatex.com-2a23505f13b76aa154ef86a4c0220c18_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds and quicklatex.com-a3b02819cd7bd2aa97cce4580437d1a7_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds for the velocity and acceleration of a particle moving with uniform speed in a circle or radius quicklatex.com-95d7c225dd31ad7d6dd5fb9f0980b531_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds.

Assuming that the moon travels in a circular orbit whose radius is quicklatex.com-0db42ac61b94a1458e59fcbe6f0c872e_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds cm. and whose centre ie the center of the earth, and completes a revolution every quicklatex.com-8e26e4950a5e29461c8c408657d51060_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds seconds, calculate the ratio of its acceleration quicklatex.com-b847d7a86faaecb70586863b64f0699c_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds towards the centre of the earth to gravity quicklatex.com-32a1fff034751d4fc3e4edc15ca376af_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds at the earth’s surface.

Question 3

Two indentical cars quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds each quicklatex.com-3c4de7b9ce82b47f9788dc2416e4c750_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds feet in length travel with constant velocity quicklatex.com-5710ac6ade182d0ad850e6efd2e4a189_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds feet per second along a straight level road, the front of quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds being quicklatex.com-03a099fb35686761d3247ea18a036180_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds feet directly behind the rear of quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds. Immediately on reaching a line drawn across the road perpendicular to the direction of motion of the cars each car decelerates at quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds feet per secquicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds.

(i) Show that quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds crashes into quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds.

(ii) At what distance from the line does the crash occur?

Question 4

An aeroplane quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds about to drop a bomb on a small stationary target quicklatex.com-6460d10729af641188d49a36153c8def_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds. on the sea surface descends along a line which is inclined at an angle of quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds to the horizontal and which passes directly over the target at a vertical height of quicklatex.com-294859fdbb1fdda439ec2363e11fdfa1_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds mile. If the aeroplane travels at quicklatex.com-756d205977874d6e3a71918445be01f5_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds m.p.h. what duration of time must elapse between the release of the bomb and its impact on the target. (See diagram).

HAM-1968-Q4-300x182 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds

Question 5

Show that the work done by a body in coming to rest is the kinetic energy of the moving body. A body of mass quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds lbs. sliding on a rough horizontal plane with initial velocity quicklatex.com-ae688913a749c2b1ee1631da8f880525_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds feet secquicklatex.com-6f9ce87bda46097b1411071acdf362b7_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds. is brought to rest by friction in quicklatex.com-8a0f60b8ca3ec09a3984d53508863c9a_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds feet. Calculate the coefficient of friction.

At what average rate in horse-power was work done on the body in bringing it to rest?

Question 6

A particle executes simple harmonic motion with a frequency of quicklatex.com-5710ac6ade182d0ad850e6efd2e4a189_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds vibrations per second. The amplitude is quicklatex.com-a740037f818c3f0104a245035116aaa8_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds millimetres.

Find (i) the maximum speed of the particle,

(ii) the maximum acceleration of the particle.

If the cutting-head of an electric razor has mass quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds grams and oscillates with simple harmonic motion at a frequency of quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds vibrations per second, and with an amplitude of quicklatex.com-a740037f818c3f0104a245035116aaa8_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds millimetres, calculate the maximum value of the driving force.

Question 7

A train is rounding a circular curve of radius quicklatex.com-c56abbec0d3913124ffb3d82e4b46ab3_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds yards. A bob hangs at one end of a light string which is fixed in the ceiling of a carriage and which is inclined at an angle of quicklatex.com-afb400442b40c1c08d63debfdacb43d0_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds to the vertical. Estimate the speed of the train.

Question 8

A fire-engine raises quicklatex.com-0a7d1908dc17ba7c399644cfaecdaeba_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds gallons of water per minute from a well quicklatex.com-3c4de7b9ce82b47f9788dc2416e4c750_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds feet deep and then pumps it as a jet issuing with a nozzle velocity of quicklatex.com-03a099fb35686761d3247ea18a036180_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds feet per sec. At what horsepower is the engine working?

Question 9

The density of lead is quicklatex.com-78989f63055c0033f93c715078525642_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds gram cmquicklatex.com-c06650c15cd2975afcf65191fe6a7e1f_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds. and that of mercury is quicklatex.com-b4a3222b53a62e3f2494ccd3d0875c9f_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds grams cmquicklatex.com-c06650c15cd2975afcf65191fe6a7e1f_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds. Explain why a block of lead will float on mercury.

A rectangular uniform block of wood floats on sea water with quicklatex.com-c1202576eb6006ba366f3dcac824fc44_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds of its volume above the water-line. What is the volume of the smallest rectangular block of the wood which will float without being totally submerged while supporting a weight of quicklatex.com-4fbb80c3d7c3c9bdfaf780287e19f597_l3 | Leaving Certificate Examination 1968 Honours Applied Mathematics | Maths Grinds lb. placed vertically above its centre of gravity?

(Take $1.03 as the specific gravity of sea-water.)


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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