Leaving Certificate Examination 1933 Honours Applied Mathematics
Question 1
The following table gives the speed of a train
seconds after leaving a station
for portion of the journey between two stations
and
,
ft. apart.
Speed in feet per second. | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
Time in seconds. | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() | ![]() |
Estimate the acceleration after seconds and the distance travelled in the
seconds. If the train continues to move with the uniform speed of
ft. per second until the brakes are applied, producing a uniform retardation of
ft. per sec. per sec., find the total time taken in going from
to
.
Question 2
(a) A particle describes simple harmonic motion of amplitude , the period being
. Prove that at distance
from its mean position its speed
is given by
.
(b) If the amplitude of the motion of bob of a simple pendulum is foot and the period
seconds, find the time occupied by the bob in passing between points which are distance
” and
” from the mean position and are on the same side of it.
Question 3
Prove that two bodies moving in different straight lines with uniform velocities will meet if their relative velocity is in the straight line joining them.
A ship steaming in a direction North of East is seen by a submarine which is in a direction
East of South from the ship. Find in what direction a torpedo travelling at
miles per hour must be fired in order to strike ship.
Question 4
A bullet of mass oz. travelling horizontally with a speed of
ft. per second becomes embedded in a block of wood of mass
lb. suspended by a light steel wire, the C.G. of the block being
ft. below the point of suspension. Find the vertical distance through which the block rises.
Question 5
When the motors of an electric train of effective weight tons are working at the rate of
H.P., a uniform speed of
miles per hour is attained on the level. Assuming the frictional resistances to remain the same, what is the maximum speed attainable with
H.P. when ascending an incline of
in
?
Question 6
Show that the centre of gravity of equal particles placed at the three vertices of a triangle respectively coincide with the centre of gravity of the area of the triangle. The parallel side of a trapezium are of lengths
and
and the perpendicular distance between them is
. Find the distance of the C.G. from the side
.
Question 7
What are the laws of solid friction?
A body of weight is dragged along a horizontal plane, coefficient of friction
, by a cord inclined at an angle
to the horizontal; find the tension in the cord. For what value of
is the tension a minimum? A body is placed on a plane, coefficient of friction
inclined at
to the horizontal; find the velocity acquired in one second.
Question 8
A triangular roof-truss has a horizontal span
of
feet and angle
is
,
and
being of equal length. The roof-truss is hinged at
and simply supported on rollers at
(so that the supporting force at
is vertical). It is loaded as follows:
tons perpendicular to
at its mid-point at
. Find the reactions of the supporting forces at
and
and the tensions in
.
Question 9
A body of weight lb. is moving due East with a velocity of
ft. per second, and forty seconds later it is moving North-East with a velocity of
ft. per second. What is the change in velocity? What constant force acting during the interval would produce the change? Show that in the latter case the hodograph is a straight line.
Question 10
Assuming that the wheels of a motor-car are feet in diameter, what is the angular velocity of a wheel when the car s travelling at the rate of
miles per hour? What is the velocity of a point on the surface of tyre (a) when vertical above the centre, (b) when the radius from the point to the centre is inclined at an angle of
to the upward vertical? What would be the force acting on a stud of mass
oz. embedded in the type when at its greatest height?
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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