Leaving Certificate Examination 1943 Honours Applied Mathematics
Question 1
Two ships 
and 
are 
miles apart, being due west of and steaming due East at 
miles per hour. is steaming due North at 
miles per hour. When will they be nearest one another and what will be their distance apart at that time?
Question 2
A particle slides down a smooth inclined plane feet long in 
seconds : find its acceleration and the inclination of the plane to the horizontal.
How far from the bottom should a second particle be started on the plane one second after the first had started from the top so that the two particles will reach the bottom together?
Question 3
On a rectangular sheet of iron, inches by 
inches, marks are made on two adjacent edges at a distance of 
inches from one corner. These marks are joined by a straight line and the sheet folded down along this line. Find the centre of gravity of the sheet so folded.
Question 4
Describe any method by which the acceleration due to gravity may be determined experimentally. Mention the causes of error likely to affect the result.
Question 5
An object of lb. wt. is placed upon a sheet of glass resting on a horizontal table and a string attached to the object passes horizontally over a pulley at the end of the table. When a weight of 
lb. is hung on the free end of the string, the object is drawn from rest through a distance of 
feet in seconds. Find the coefficient of friction between the object and the glass and also the tension in the string.
Question 6
A uniform iron bar 
, 
ft. long, weighs lb., has a lb. weight fixed to it at a point 
ft. from , and is supported by means of cords attached to its ends from a peg 
. The cord 
is 
ft. long and the cord 
is ft. long. Find the inclination of the bar to the horizontal in the position of equilibrium and find the tensions in the cords.
Question 7
The height of a lift from the ground 
seconds after starting is 
feet, given by the following table :-
| | | | | | |  |  | | |  | |
|---|---|---|---|---|---|---|---|---|---|---|---|---|
|  |  |  |  |  |  |  |  |  |  |  |  |
Draw the distance-time graph for the lift. Find the greatest velocity of the lift.
Draw a rough velocity-time graph, and use it to give a short account of the variation in the acceleration throughout the journey.
Question 8
An inverted cone, of angle 
, has a smooth inside surface and rests with its axis vertical. A smooth particle moves in a horizontal circle on the inside of the cone with a uniform speed of feet per second. Find the distance of the particle from the vertex of the cone.
Question 9
A particle is moving in a straight line with Simple Harmonic Motion. When it is ft. and ft. from the centre of its path, its speed are 
ft./sec. and ft./sec. respectively. Find the period and the amplitude of the motion. Find also the maximum speed and the maximum acceleration of the particle.
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/
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