My Journal

All things Mathematical
27Sep2018

Leaving Certificate Examination 1942 Honours Applied Mathematics

/
Posted By
/
Comments0
Question 1

A warship steaming due North at quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds knots is observed by a submarine quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds sea-miles North-West of her. The submarine has a speed of quicklatex.com-8a0f60b8ca3ec09a3984d53508863c9a_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds knots. In what direction should the submarine steer to close in one the warship as soon as possible? If she follows that course how long will it take her to get within one sea-mile of her quarry?

[One knot=one sea-mile per hour.]

Question 2

Three particles whose masses are in the ratio quicklatex.com-9b49097f78e079a55a50343707575283_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds are in motion in a plane. Referred to rectangular axes in the plane, their co-ordinates are quicklatex.com-98782a30e844fed3d1757a964590b3d1_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds; quicklatex.com-d9807a9453aca6bfe89ea6876b2a376b_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds; quicklatex.com-85846d52806f96062e9d9e46d350bde1_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds respectively at time quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds. Find the co-ordinates of the centre of gravity of the particles at time quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds and show that it is moving with constant velocity.

Question 3

How far will a body travel if projected horizontally along ice at an initial velocity of quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds metres per second, the coefficient of friction being quicklatex.com-a6e4fa5ef3f18d83d47f3cb220156be3_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds?

If after quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds seconds the body collides directly and combines with a similar body of equal mass resting on the ice, how far will the joint masses proceed together after coalescing?

[Answer in each case to the nearest metre.]

Question 4

(a) Show how the centre of gravity of a uniform lamina in the form of a quadrilateral can be found by geometrical construction.

(b) A heavy rod quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds feet long has its centre of gravity quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds foot from one end and is suspended by a string quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds feet long attached to its ends and passing over a smooth peg. Find, graphically or otherwise, the inclination of the rod to the horizontal in the position of equilibrium.

Question 5

A ball was kicked so as to leave the ground at quicklatex.com-5710ac6ade182d0ad850e6efd2e4a189_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds feet per second and struck a bar which was quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds feet high and quicklatex.com-7260fe4f20eb47e11e44b79da133e21c_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds feet away. Find the two possible values of the angle of projection of the ball.

Question 6

Explain the terms amplitude, period, phase as applied to Simple Harmonic Motion.

Show that a point moving in a straight line and whose distance quicklatex.com-ada3765a264ac03a253ee0ccbe61f602_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds, at time quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds, from a fixed point in the line is given by quicklatex.com-c779cbaa12d754b7b00659982949bb29_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds, where quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds, quicklatex.com-6fd4a229a60f10645306b68a0a0ee2e6_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds are constants, is in S.H.H. Show that the velocity is greatest at the fixed point and find an expression for the period.

Question 7

When a particle is moving in a circle with uniform speed quicklatex.com-8bafe7d16e660869fc203e8bffd77abc_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds, prove that its acceleration is quicklatex.com-fd7c71cce7559f4f0ead815793016715_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds towards the centre of the circle.

A swing is made up of a seat of quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds lb. wt. supported by two ropes each quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds ft. long. When the swing is carrying a boy of quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds stone wt. through an angle of quicklatex.com-43254279a766115b4c8c77b4f9e086ff_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds on each side of the vertical find the tension in each rope (i) at the highest, (ii) at the lowest position of the seat.

[Neglect weight of ropes.]

Question 8

The engine of a ton lorry is quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds H.P. When the lorry is travelling at quicklatex.com-66bafba23129fa8ab0a7d7fd2fc25d52_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds miles per hour up an incline of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds in quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds it is accelerating at the rate of quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds ft./sec.quicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds; find the total frictional resistances to the motion. At what rate does the lorry accelerate when travelling down an incline of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds in quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds at quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1942 Honours Applied Mathematics | Maths Grinds miles per hour, assuming that the frictional resistances are the same and that the engine is working at full power in both cases?

 


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.