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21 Jun 2019

Leaving Cert Applied Maths Higher Level 1976

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Question 1

(a) Show that, if a particle is moving in a straight line with constant acceleration quicklatex.com-66c806215945e3dc90f658b54f6dcae9_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and initial speed quicklatex.com-ba05715987b9d18252648b0ecfc8eb72_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, the distance travalled in time quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds is given by quicklatex.com-4578e82d80aa1fb562a4e61a8cb95320_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds.

(b) Two points quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and quicklatex.com-91dc9a245a0f25a550d41a6feb58273f_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds are a distance quicklatex.com-7e66f8d3fbb50779ceb68e5184deb32d_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds apart. A particle starts from quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and moves towards quicklatex.com-91dc9a245a0f25a550d41a6feb58273f_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds in a straight line with initial velocity quicklatex.com-ba05715987b9d18252648b0ecfc8eb72_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and constant acceleration quicklatex.com-66c806215945e3dc90f658b54f6dcae9_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds A second particle starts at the same time from quicklatex.com-91dc9a245a0f25a550d41a6feb58273f_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and moves towards quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds with initial velocity quicklatex.com-8371b75eaeac9a5a537b75fe200ca458_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and constant deceleration quicklatex.com-66c806215945e3dc90f658b54f6dcae9_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds. Find the time in terms of quicklatex.com-ba05715987b9d18252648b0ecfc8eb72_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, quicklatex.com-7e66f8d3fbb50779ceb68e5184deb32d_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds at which the particle collide, and the condition satisfied by quicklatex.com-ba05715987b9d18252648b0ecfc8eb72_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, quicklatex.com-66c806215945e3dc90f658b54f6dcae9_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, quicklatex.com-7e66f8d3fbb50779ceb68e5184deb32d_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds if this occurs before the second particle returns to quicklatex.com-91dc9a245a0f25a550d41a6feb58273f_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds.

Question 2

A particle is projected upwards with a speed of quicklatex.com-6fa002e1799dcb54bc79a06dc47ef0af_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds m/s from a point quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds on a plane inclined at quicklatex.com-9c3fb28be0c20ddb0b2c4bd59c303de8_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds to the horizontal. The plane of projection meets the inclined plane in a line of greatest slope and the angle of of projection, measured to the inclined plane, is quicklatex.com-b3e30721015b16e23fa7c14ec02c70c2_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds.

(i) Write down the velocity of the particle and

(ii) its displacement from quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, in terms of quicklatex.com-f453dfa2ac10361897075d9950ad4c04_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and quicklatex.com-be4ffaf4d71dac859eb0823be8c6649f_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, after time quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds seconds.

(iii) If the particle is moving horizontally when it strikes the plane at quicklatex.com-8859b07193d4c340b17f3853ff89fdaa_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds prove that quicklatex.com-c9db3f991148d6e7ab23c3fd79a6fb41_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and

(iv) calculate quicklatex.com-7570fd0ddff53affcb58baa89d325060_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds.

Question 3

The diagram shows a light inelastic string, passing over a fixed pulley quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, connecting a particle quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds of mass quicklatex.com-e20b49f19ccabffb1d8e0d926f339dc7_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds to a light movable pulley quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds. Over this pulley passes a second light inelastic string to the ends of which are attached particles quicklatex.com-e24826b0fac28861acd034428af346f0_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, quicklatex.com-7b14fa9f950652c6b6f4cfa6074d7021_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds of masses quicklatex.com-fce5a805c0f6f0bd2d059819c56bf93a_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, quicklatex.com-941d689ad0e65c5d5733efadca408734_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds respectively.

(i) Show in separate diagrams the forces acting on quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, quicklatex.com-e24826b0fac28861acd034428af346f0_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and quicklatex.com-7b14fa9f950652c6b6f4cfa6074d7021_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds.

(ii) Write down the three equations of motion involving the tensions quicklatex.com-6460d10729af641188d49a36153c8def_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, quicklatex.com-e0f17e01fb67b2164e7656895346ce8b_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds in the strings, the acceleration of quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and the common acceleration of quicklatex.com-e24826b0fac28861acd034428af346f0_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, quicklatex.com-7b14fa9f950652c6b6f4cfa6074d7021_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds relative to quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds.

(iii) Show that quicklatex.com-6225918f06fc3c0e23791aacde38a5ba_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds.

HAM-1976-Q3-225x300 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds

Question 4

A light smooth ring of mass quicklatex.com-941d689ad0e65c5d5733efadca408734_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds is threaded on a smooth fixed vertical wire and is connected by a light inelastic string, passing over a fixed smooth peg at a distance quicklatex.com-7e66f8d3fbb50779ceb68e5184deb32d_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds from the write, to a particle of mass quicklatex.com-fce5a805c0f6f0bd2d059819c56bf93a_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds hanging freely. The system is released from rest when the string is horizontal. Explain why the conservation of energy can be applied to the system. If the ring descends a distance of quicklatex.com-ada3765a264ac03a253ee0ccbe61f602_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds while the particle rises through a distance quicklatex.com-bf6617d66346a8bf69ba3489970c8733_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds

(i) show that

quicklatex.com-9d3f095cf61359faaba459efff542fdb_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and quicklatex.com-259f00b5fdb5dee80c9faf5fcc5136a8_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds

where quicklatex.com-2c3503dd111a2205ad05bf7046c99d75_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, quicklatex.com-67f763deeac60cc94a57f9a9ebb3442d_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds are the speeds of the ring and particle respectively.

Find quicklatex.com-514a143a88734dd83edd3419d47de51c_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds when

(ii) quicklatex.com-c6a72097ed4ef9eb867a70e459bbb26d_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and

(iii) when quicklatex.com-1b8c2773e944e5485f606ecdb9eafc1c_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds.

Question 5

(a) State the laws governing the oblique collisions of elastic spheres.

(b) A sphere of mass quicklatex.com-941d689ad0e65c5d5733efadca408734_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds moving with speed quicklatex.com-ba05715987b9d18252648b0ecfc8eb72_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds collides obliquely with a second smooth sphere at rest. The direction of motion of the moving sphere is inclined at quicklatex.com-9c3fb28be0c20ddb0b2c4bd59c303de8_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds to the line of centres at impact, and the coefficient of restitution is quicklatex.com-294859fdbb1fdda439ec2363e11fdfa1_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds. After impact the directions of motion of the spheres are at right angles.

Find the mass of the second sphere in terms of quicklatex.com-941d689ad0e65c5d5733efadca408734_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, and the velocities of the two spheres after impact in terms of quicklatex.com-ba05715987b9d18252648b0ecfc8eb72_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds. Hence show that one quarter of the kinetic energy is lost.

Question 6

Two uniform rods quicklatex.com-819964b5440e1d7a1941259fada7d9c6_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, quicklatex.com-93cd9fa3dc459ef3d77cd955c6c49da5_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds of lengths quicklatex.com-0e440a33f92d8dd692a299e70ffc00e6_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, quicklatex.com-97c2e13119b2390bcef4a121da207258_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and of weights quicklatex.com-d993c85fe0de1c28d00ef58f0653f60d_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, quicklatex.com-f4025cee76bd72cf99c85b78b51daf0c_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds respectively are smoothly hinged together at quicklatex.com-91dc9a245a0f25a550d41a6feb58273f_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds. They stand in equilibrium in a vertical plane with the end quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds resting on rough horizontal ground and the end quicklatex.com-5403eeae09f3e9689d2ad28aa6fe1599_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds resting against a smooth vertical wall. The point quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds is farther from the wall than quicklatex.com-91dc9a245a0f25a550d41a6feb58273f_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and the rods quicklatex.com-819964b5440e1d7a1941259fada7d9c6_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, quicklatex.com-93cd9fa3dc459ef3d77cd955c6c49da5_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds are inclined at angles quicklatex.com-0dce58ae1ea930bb9c39e85ab5e4c977_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, quicklatex.com-9c3fb28be0c20ddb0b2c4bd59c303de8_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds respectively to the horizontal where quicklatex.com-46dfb81e4eebe02042ea384ca3911f6b_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds.

(i) Show in separate diagrams the forces acting on each rod.

(ii) By considering separately the equilibrium of the system quicklatex.com-11c6fd2690294ef6f792ee277004059b_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and the rod quicklatex.com-93cd9fa3dc459ef3d77cd955c6c49da5_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, find the coefficient of friction at quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and

(iii) show that quicklatex.com-4308fba55cd96b07490aef737c26e857_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds.

Question 7

(a) Define simple harmonic motion.

(b) A particle of mass quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds kg is attached to the ends of two light elastic strings, each of natural length quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds m and elastic constant quicklatex.com-4f1d3075721bd7b8c0e6652c92aeb23e_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds N/m. The other ends of the two strings are attached to two fixed points quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and quicklatex.com-91dc9a245a0f25a550d41a6feb58273f_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds in the same vertical line, where quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds is quicklatex.com-fd6542ae3d49d38a0f73fefe83b285af_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds m above quicklatex.com-91dc9a245a0f25a550d41a6feb58273f_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds. The particle when is released from rest from the midpoint of quicklatex.com-819964b5440e1d7a1941259fada7d9c6_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds.

(i) By considering the forces acting on the particle when it is quicklatex.com-ada3765a264ac03a253ee0ccbe61f602_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds metres from quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, where quicklatex.com-3addde4c8565a063bd6142b2c8fc94a2_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, show that it is moving with simple harmonic motion.

(ii)Find the least time taken for the particle to reach the point quicklatex.com-a3a1e11de87404fc1c9c504a0b633f98_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, and find its speed there.

Question 8

A pendulum of a clock consists of a thin uniform rod quicklatex.com-819964b5440e1d7a1941259fada7d9c6_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds of mass quicklatex.com-941d689ad0e65c5d5733efadca408734_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and length quicklatex.com-2912efae9bab6a509e798bbd356587e9_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds to which is rigidly attached a uniform circular disc of mass quicklatex.com-701ba630cb8f3efdb2500ef85e0bdad6_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and radius quicklatex.com-7e66f8d3fbb50779ceb68e5184deb32d_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds with the centre of the disc being at the point quicklatex.com-5403eeae09f3e9689d2ad28aa6fe1599_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds on quicklatex.com-819964b5440e1d7a1941259fada7d9c6_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds where quicklatex.com-ce1d3b10b23038979401ae139230500c_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds.

(i) Using the parallel axes theorem for the disc, show that the moment of inertia of the pendulum is free to oscillate in a vertical plane about such a fixed horizontal axis at quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds.

(ii) It is released from rest with quicklatex.com-819964b5440e1d7a1941259fada7d9c6_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds horizontal. Find the speed of quicklatex.com-91dc9a245a0f25a550d41a6feb58273f_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds when quicklatex.com-819964b5440e1d7a1941259fada7d9c6_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds is vertical.

Question 9

An atomic nucleus of mass quicklatex.com-941d689ad0e65c5d5733efadca408734_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds is repelled from a fixed point quicklatex.com-2a137ec0f9eba36b0ab49cf15f39f89e_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds by a force quicklatex.com-2d3cfc4bdd445473d1536a86ae9899d0_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, where quicklatex.com-ada3765a264ac03a253ee0ccbe61f602_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds is the distance of the nucleus from quicklatex.com-2a137ec0f9eba36b0ab49cf15f39f89e_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and quicklatex.com-66c806215945e3dc90f658b54f6dcae9_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds is a constant. It is projected directly towards quicklatex.com-2a137ec0f9eba36b0ab49cf15f39f89e_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds with speed quicklatex.com-1cac07508b14981b5d5190a58b0eca69_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds from a point quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds where quicklatex.com-4841cfa5d2671aaf2afe2f01fc6101d4_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds. Find the speed of the nucleus when it reaches the midpoint of quicklatex.com-aacec3d65b3492ccb556138aeb74601a_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and find how near it gets to quicklatex.com-2a137ec0f9eba36b0ab49cf15f39f89e_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds.

Question 10

(a) Using Taylor’s theorem find the first two terms in the Taylor series for quicklatex.com-85b7b0af6448bc21148f2bc2003dd0ea_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds in the neighborhood of quicklatex.com-4b059b7e799e27edffd890d114f605d4_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, i.e. the Maclaurin series for quicklatex.com-9138788c29150e987b19720c786e937c_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds.

(b) State Archimedes principle for a body wholly or partly immersed in a liquid.

(c) A uniform thin rod is of length quicklatex.com-7ff41b23cb36059c55f89f7da3a641a8_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds, of weight quicklatex.com-8a1cbd76278fe4548e551c88bbb5f3af_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds and specific gravity quicklatex.com-ac9cf4ec1486ec33eaf338322bf214be_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds. The rod rests in equilibrium in an inclined position partly immersed in water with its lower end freely pivoted to a fixed point at depth quicklatex.com-95557400c8dd49246fa5075ed92ecde7_l3 | Leaving Cert Applied Maths Higher Level 1976 | Maths Grinds below the surface of the water. Show in a diagram the forces acting on the rod and calculate the inclination of the rod to the vertical.


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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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