My Journal

All things Mathematical
17Oct2018

Leaving Certificate Examination 1950 Honours Applied Mathematics

/
Posted By
/
Comments0
Question 1

If the velocities of two bodies quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds are known, indicate by means of a diagram, or otherwise, how the velocity of quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds relative to quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds may be found.

When a man is travelling due east at quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds miles per hour, the wind appears to blow from the north, but when he is travelling north east at quicklatex.com-3c4de7b9ce82b47f9788dc2416e4c750_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds miles per hour, it appears to blow from a point quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds east of north. Find the velocity of the wind in magnitude and direction.

Question 2

Two masses, quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds, weighing quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds lb. and quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds lb. respectively, are connected by means of a light string passing over a smooth pulley. quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds is at rest on the floor and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds is handing freely. The mass quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds is raised a vertical distance of quicklatex.com-2b18fa15a2f284d990fd81b9cae524ce_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds feet and is then allowed to fall freely. Find how logn after it has been jerked into motion it will take the mass quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds to return to the floor. Find, also, the kinetic energy of the system immediately before, and immediately after, the mass quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds is jerked into motion.

Question 3

An engine is travelling round a curve of radius quicklatex.com-67eec091c6b1a71104211ea29b6f63be_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds feet on a horizontal railway track, the rails of which are at the same level and quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds feet apart. If the centre of gravity of the engine is quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds feet above the level of the rails and is in vertical plane which bisects the distance between them, find the greatest speed wt which the engine can travel found the curve without losing contact with one of the rails.

Find, also, the distance which the outside rail must be raised so that there may be no lateral thrust on the rails when the engine is travelling at quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds milers per hour.

Question 4

One end of a uniform ladder, weighing quicklatex.com-5710ac6ade182d0ad850e6efd2e4a189_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds lb., rests on a rough plane inclined at angle of quicklatex.com-209c1958604e9f7d31e020b608033e83_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds to the horizontal, and the other end rests against a smooth vertical wall at the top of the plane. The coefficient of friction between the ladder and the plane is quicklatex.com-e3fbd8f0215ac5813f0661c26cc6f329_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds. If the ladder is one the point of slipping, find its inclination to the wall, also, its total reaction on the plane.

Question 5

A train, starting from rest at the bottom of an incline of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds in quicklatex.com-094ee6d517670326a569d5b0dc00b494_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds and moving with uniform acceleration, attains a speed of quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds miles per hour when it has travelled one mile up the incline. If the engine weighs quicklatex.com-cbbca562b8a27132c102a81b44b1362d_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds tons and the rest of the train quicklatex.com-bd7202b6cf8beeda1b46bb2799ac945c_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds tons, and if the resistances to motion are equivalent to quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds lb. wt. per ton, find the tension in the coupling between the engine and the rest of the train. Find, also, the H.P. at which the engine is working when the train attains the speed of quicklatex.com-7bc4f1f0f4c11887bbe547ac256853e5_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds miles per hour up the incline.

Question 6

A piece of metal of uniform thickness is in the shape of a square of side quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds inches together with an isosceles triangle whose base is one od sides of the square. The centre of gravity of the piece of metal is in the base of the isosceles triangle. The top of the triangular portion is removed by cutting along a line which joins the middle points of the equal sides of the isosceles triangle. Find how far the centre of gravity of the remaining piece is from the intersection of the diagonals of the square.

Question 7

The side-wall of a house is quicklatex.com-a596ad4d5102039f1aaadb9079aa1b05_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds feet high, and the roof which is smooth makes an angle of quicklatex.com-f643069adb772a4896813c16b313ad05_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds with the horizontal. An object on the roof slides from rest at a point quicklatex.com-3c4de7b9ce82b47f9788dc2416e4c750_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds feet from the bottom edge down along the line of greatest slope and then falls freely to the ground. With what velocity, in magnitude and direction, and how far from the bottom of the side-wall, will the object strike the ground?

Question 8

What do you understand by “simple harmonic motion”?

When a particle moving with simple harmonic motion is travelling towards its mean position and is at a distance of quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds feet from it, its velocity and acceleration are quicklatex.com-8a0f60b8ca3ec09a3984d53508863c9a_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds feet per sec. and quicklatex.com-8a0f60b8ca3ec09a3984d53508863c9a_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds feet per sec.quicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds, respectively. Find (a) the amplitude, (b) the periodic time, (c) the least time it will take the particle to reach its mean position.

Question 9

The walls of a rectangular swimming bath are vertical and the floor slopes uniformly so that the water is quicklatex.com-ee873c946a42a316d07b2d164e2b7d67_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds feet deep at one end and quicklatex.com-ced9adf500abe3e625f021cf18429a9e_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds feet deep at the other end. The bath is quicklatex.com-88c065fecf0554f2316700e1f2bf361f_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds feet long and quicklatex.com-5710ac6ade182d0ad850e6efd2e4a189_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds feet wide. Find the total thrust of the water (a) on the wall at the deep end, (b) on one of the side-walls.

A line drawn parallel to the surface of the water on the wall at the deep end divides the wall into two portions, the thrusts on which are equal. Find how far the line is below the surface of the water.

[quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Certificate Examination 1950 Honours Applied Mathematics | Maths Grinds cu. ft. of water weighs quicklatex.com-96052cd1530c9b803b2359dea67ec819_l3 | Leaving Certificate Examination 1950 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:

“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.