152
LEAVING CERTIFICATE, 1888.
11. If y2=4a;c be the equation to a parabola and {h, k) be a point on
the curve, find the equations to the tangent and normal at that
point.
12. If a, (3, and y be the perpendicular distances of a point P from the
sides of a triangle, investigate the meaning of the equations
a—p=0, p—7=0, y—a=0, a + /3=0, a + /3 + y=0.
No. 6.—DYNAMICS.
Monday, 25th June. 3 p.m. to 5 p.m.
Give your working in full.
Endeavour rather to answer a moderate number of questions accu¬
rately and fully than to answer a large number imperfectly.
1. Define Velocity. How is Uniform Velocity measured ?
Two men ride along two roads at right angles, at the rates of
five miles an hour and 12 miles an hour. Find the velocity of
one relatively to the other.
2. A body falls from rest with uniform acceleration g. Find the
equations of motion.
If <7=32/2, find the length moved in 41 seconds.
3. State Newton’s three Laws of Motion.
4. Forces acting at a point are represented in magnitude and direction
by three sides of a quadrilateral figure taken in order. Find
their resultant. Show whether your proof holds good if the
angular points are not all in one plane.
5. Find the resultant of two parallel forces acting in similar directions
at two points of a rigid body.
A rod, two feet long, weighs one pound, and has masses of one
and three pounds hanging from its extremities. Where must it
be supported so as to balance ?
6. Define Centre of Gravity, and find that of a parallelogram.
What other names have been given to the Centre of Gravity ?
Part of a parallelogram is cut off by joining the middle points
of two adjacent sides. Find the centre of gravity of the
remainder.
7. Describe one form of steel-yard.
8. A mass of one ton rests on a smooth plane which rises 2 in 5.
What horizontal force is required to keep the mass .from
slipping ?
Optional Questions.
9. Define work. How is it measured ?
How much work is done by a man of 12 stone (1) in climbing
a hill 800 feet high, (2) in walking a mile along a level road ?
What considerations are neglected in your calculation ?
10. Give the laws of Statical Friction.
What is the Angle of Repose ? Give any instance of its occur¬
rence in Nature.