Leaving Certificate Examination 1961 Honours Applied Mathematics
Question 1
is a triangle in which 
, 
, 
. Forces of 
, 
, 
lb. wt. act along 
, 
, 
, respectively. How far from 
does the line of action of their resultant cut ?.
Find the magnitude of the resultant in lb. wt., correct to one place of decimals, and find the angle which its line of action make with , correct to the nearest degree.
Question 2
Explain the terms “limiting friction,” “coefficient of friction.”
When a truck is ascending an incline of 
in 
with a uniform acceleration of 
ft. per sec. per sec., a box on the floor of the truck is just about to slide backwards. Show by diagram the forces acting on the box, and find the coefficient of friction between the box and the floor of the truck.
Question 3
A man is cycling at 
m.p.h. in a steady wind. When he cycles in a direction 
north of east the wind appears to him to blow directly from the east. When he cycles due east the wind appears to him to blow from the south-east. Find the velocity of the wind in magnitude and direction.
Question 4
Two bodies, of mass 
gm. and 
gm. respectively, are lying on a smooth horizontal bench which is 
feet high. The gm. body is at the edge of the bench and the gm. body is 
feet away in a direction perpendicular to the edge, the bodies being connected by a light inextensible string 
feet long. If the gm. body is pushed gently over the edge, find how many seconds later it will reach the ground.
Question 5
Derive an expression for the total time of flight of a projectile in terms of its initial velocity and angle of projection.
, , 
, are three collinear points on a horizontal plane. A projectile fired from passes over at a height of 
feet and reaches its greatest height as it passes over . If 
feet and the total time of flight of the projectile is 
seconds, find its initial velocity.
Question 6
A mass of lb. suspended from a fixed point by a light inextensible string 
feet long acts as a conical pendulum, the mass describing a horizontal circle at a uniform rate of 
revolutions per minute. Find the tension in the string, in lb., wt., and the inclination of the string to the vertical.
Question 7
A particle is moving along a straight line so that is distance 
(cms.) from a fixed point 
at the time 
(secs.) is given by the formula
.
Show that the motion is simple harmonic and find the periodic time and the maximum velocity.
If the velocity of the particle at 
is 
cm. per sec., find its acceleration at , and find the least time the particle takes to travel to from .
[See Tables, p. 30].
Question 8
A triangular lamina is immersed in a liquid of specific gravity 
so that the vertex is at the surface and the sides 
is vertical. If 
, 
, 
, find the thrust of the liquid on in ounces.
is a point on such that the thrust of the liquid on 
is give-ninths of the thrust on . Find the length of 
.
[A cubic foot of water weights 
lb.]
Question 9
is a quadrilateral lamina in which 
, 
, , 
. Find the perpendicular distance of the centre of gravity of from .
Find, also, the perpendicular distance of the centre of gravity of 
from 
.
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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