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3 Jul 2019

Leaving Cert Applied Maths Higher Level 1978

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Question 1

A driver starts from rest at quicklatex.com-d613350484b582bc83e2a6f9473437f8_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and travels with a uniform acceleration of quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds m/squicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds for quicklatex.com-6460d10729af641188d49a36153c8def_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds seconds. He continues with uniform velocity for quicklatex.com-089743ef85116e345b464909a7938217_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds seconds, and then decelerates uniformly to rest at quicklatex.com-6ce7c226153d55058c10348c6739a4c5_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds  in a further quicklatex.com-f922abf1c4d6e4e32bf00b68e88bb4de_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds seconds. Express the distance quicklatex.com-e979ae05a61debd12da167a83e2720d6_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds in terms of quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and quicklatex.com-6460d10729af641188d49a36153c8def_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds.

Another driver can accelerate at quicklatex.com-7ff41b23cb36059c55f89f7da3a641a8_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds m/squicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and can decelerate at quicklatex.com-f2a4ac98b02973c931354853746bb790_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds m/squicklatex.com-025303222356a63c2332a429c33d35a9_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds. Find, in terms of quicklatex.com-6460d10729af641188d49a36153c8def_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds, the least tiem in which this driver can cover the distance quicklatex.com-e979ae05a61debd12da167a83e2720d6_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds from rest to rest

(i) subject to a speed limit of quicklatex.com-152527a51d6f5e3abc04c18d5e853e52_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds m/s,

(ii) subject to a speed limit of quicklatex.com-f50b4f03912ec56685a20aece0ea16e2_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds m/s.

Question 2

A plane is inclined at an angle quicklatex.com-0dce58ae1ea930bb9c39e85ab5e4c977_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds to the horizontal. A particle is projected up the plane with initial velocity quicklatex.com-ba05715987b9d18252648b0ecfc8eb72_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds at an angle quicklatex.com-d6ffefedf9d4e7e4f42ba65b9f3b9416_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds to the plane. The plane of projection is vertical and contains the line of greatest slope.

(i) Write down the displacement and velocity of the particle parallel and perpendicular to the plane at time quicklatex.com-db2144d676b0c010fa61116d07db1982_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds.

(ii) Show that the time taken by the particle to reach its maximum perpendicular height above the plane is half the time of flight up the plane.

(iii) When the particle is at its maximum perpendicular height above the plane, the distance travelled parallel to the plane is quicklatex.com-93ba715eab64d4939af4318b719cde8b_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds of the range up the plane. Show that in that case quicklatex.com-3ab4090f40d647b150dbfb7670184c21_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds.

Question 3

(i) Two vectors quicklatex.com-57ac8a5549bfd627065ab8fa45e00586_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and quicklatex.com-d45f78337a1dddd8929ef5c5a353be86_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds are at right angles. Write down the condition satisfied by the scalars quicklatex.com-5c5226745fc0b9dfd6c3b0e3045b593d_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds.

(ii) Two smooth spheres of masses quicklatex.com-7a02bd7300eeadcf269af0186938941e_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and quicklatex.com-bc90a078f248740eba6949305c963ffc_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and velocities quicklatex.com-ba05715987b9d18252648b0ecfc8eb72_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and quicklatex.com-8bafe7d16e660869fc203e8bffd77abc_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds, respectively, collide as shown in the diagram, where quicklatex.com-dc95b4619aefb4012b1e4548e50c9741_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds. The sphere of mass quicklatex.com-7a02bd7300eeadcf269af0186938941e_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds is deflected through an angle of quicklatex.com-a167991e6500d652c6496c53e44145a7_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds by the collision. If the coefficient of restitution is quicklatex.com-a94f7602fb0c8f60ddf34329136f92e1_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds, show that quicklatex.com-3e8bce41617ddbc8be089cce29d91bd8_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds.

(iii) Find the direction of motion of the other sphere after the collision.

HAM-1978-Q3-300x273 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds

Question 4

A body of mass quicklatex.com-89639d0e0a022372a0e71343e544680b_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds lies on a smooth horizontal table. It is connected by means of a light string passing over a smooth light pulley at the edge of the table, to a second smooth pulley of mass quicklatex.com-e4fec7c727c9e630af2cfb5a79ea65c7_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds hanging freely. Over this second pulley passes another light string carrying masses of quicklatex.com-bc90a078f248740eba6949305c963ffc_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and quicklatex.com-7cb823db1803308b48e12a0a81f5d555_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds (see diagram).

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

(ii) Write down the equations of motion involving the tensions quicklatex.com-6460d10729af641188d49a36153c8def_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and quicklatex.com-e0f17e01fb67b2164e7656895346ce8b_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds in the strings, the common acceleration quicklatex.com-7bb38d45d3423fb2637bab5a782e97f1_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds of the quicklatex.com-89639d0e0a022372a0e71343e544680b_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and quicklatex.com-e4fec7c727c9e630af2cfb5a79ea65c7_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds masses and the common acceleration quicklatex.com-84fdf06eaf2b99889abd1c8acdc13d5f_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds of the quicklatex.com-7cb823db1803308b48e12a0a81f5d555_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and quicklatex.com-bc90a078f248740eba6949305c963ffc_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds masses relative to the quicklatex.com-e4fec7c727c9e630af2cfb5a79ea65c7_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds mass.

(iii) Show that quicklatex.com-0d1638d8799b06dcc74227e2d5b4f9e1_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds.

HAM-1978-Q4-300x300 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds

Question 5

Two uniform rods quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and quicklatex.com-3675ba693016b80ac93fbf734e15678b_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds of equal length and of masses quicklatex.com-dc2e717421b16a9f080dba4c8c0e3437_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds kg and quicklatex.com-1ee1c2caec46fc384f9e0e830a2e8b84_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds kg, respectively, are freely hinged at quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds. quicklatex.com-bb11fdb4c82e898ea8147471416d775f_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and quicklatex.com-3675ba693016b80ac93fbf734e15678b_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds are in a vertical plane and the ends quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds are on a rough horizontal plane. The coefficient of friction between each rod and the plane is the same.

(i) Find the normal reactions at quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds.

(ii) The angle quicklatex.com-0583d6d2788896443d34c799ae91c2df_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds is increased until one of the rods begins to slip. Show that slipping will first occur at quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds rather than at quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds.

(iii) Find the least value of the coefficient of friction if slipping has not occurred before quicklatex.com-d9697039819ee9ede5f14bdaf4018fa4_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds.

Question 6

Two small smooth rings quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds, each of mass quicklatex.com-7a02bd7300eeadcf269af0186938941e_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds are threaded on a fixed smooth horizontal wire. They are connected by means of two light inextensible strings quicklatex.com-371fe833e9a89e2790fc66adb618b944_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and quicklatex.com-3675ba693016b80ac93fbf734e15678b_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds, each of length quicklatex.com-ce939b244df556d77c12e315c6165e7d_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds metres, to a particle of mass quicklatex.com-bc90a078f248740eba6949305c963ffc_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds hanging freely at quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds. quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds, quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds,quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds are in the same vertical plane. The system is released from rest with the angles quicklatex.com-cdf5830ec07bfe79f465775f8df84302_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds.

(i) If quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds travels a horizontal distance quicklatex.com-ada3765a264ac03a253ee0ccbe61f602_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds while quicklatex.com-e86ae6aeacc8696c140ee1ca29d51f96_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds falls a vertical distance quicklatex.com-bf6617d66346a8bf69ba3489970c8733_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds, show from geometry that quicklatex.com-90593d37052cf9bc1f3b6175aa3748d3_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds.

(ii) By differentiating find quicklatex.com-c7e123db1b12abbfd0d82d522e314109_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds in terms of quicklatex.com-ada3765a264ac03a253ee0ccbe61f602_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and quicklatex.com-bf6617d66346a8bf69ba3489970c8733_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds, where quicklatex.com-514a143a88734dd83edd3419d47de51c_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds means quicklatex.com-38caa79155b98346c17aecb7e801851a_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds, and using the conservation of energy find quicklatex.com-514a143a88734dd83edd3419d47de51c_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds in terms of quicklatex.com-bf6617d66346a8bf69ba3489970c8733_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds.

(iii) Show that the velocity of quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds is quicklatex.com-fe7f3575dba1ee2794b3fb29f7ca2a28_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds where quicklatex.com-563d511dca327598420ce5802c5c48cf_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds.

Question 7

(a) Prove that the moment of inertia of a uniform circular disc about a perpendicular axis through its centre is quicklatex.com-410dabf359038a30bbe744289959527b_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds, where quicklatex.com-95d7c225dd31ad7d6dd5fb9f0980b531_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds is the radius of the disc and quicklatex.com-7a02bd7300eeadcf269af0186938941e_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds is its mass.

(b) A light string is wound around the rim of a uniform disc of radius quicklatex.com-95d7c225dd31ad7d6dd5fb9f0980b531_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and mass quicklatex.com-7a02bd7300eeadcf269af0186938941e_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds. One end of the string is attached to the rim of the disc and the other end is attached to a fixed point above the disc, with the plane of the disc vertical (see diagram). When the disc is released from rest it falls vertically and the string unwinds.

If the disc falls a distance quicklatex.com-ada3765a264ac03a253ee0ccbe61f602_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds while it turns through an angle quicklatex.com-d6ffefedf9d4e7e4f42ba65b9f3b9416_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds, show that quicklatex.com-bc5c3339e65460bbfe876bb7b0ee135c_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and deduce that quicklatex.com-99f82c7dc3f840dbe235c15455f30a2a_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds. where quicklatex.com-6fd4a229a60f10645306b68a0a0ee2e6_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds is the angular velocity of the disc. (quicklatex.com-514a143a88734dd83edd3419d47de51c_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds means quicklatex.com-01fae4b4c3ca461e2cde649a42484b19_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds, quicklatex.com-d6233ed27b7c6864dd0bb3be66409ea7_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds means quicklatex.com-3f2324b769439b83548e73aa9da1a6d7_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds)

Using the principle of angular momentum, find the tension in the string and the vertical acceleration of the disc.

HAM-1978-Q7 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds

Question 8

Solve the following differential equations:

(i) quicklatex.com-70efadf4b1dd9bb7870a84a9c5bb3786_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds if quicklatex.com-55132ac813a32dab57735b6282f1843e_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds when quicklatex.com-8ed93fef0596d8393d81a24553e60308_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds

(ii) quicklatex.com-82898b1cf982a90e1ccf75ca404c0171_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds if quicklatex.com-6f27dd9bca8028d7f339385457d1adfa_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and quicklatex.com-41925a74b8d22bf99075f418fe38785a_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds when quicklatex.com-287cbf25eabaa5b859b30410e8454f09_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds.

A particle of mass quicklatex.com-7a02bd7300eeadcf269af0186938941e_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds is acted on by a force quicklatex.com-ad5f748d6c231aab474310928ca02c3a_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds directed away from a fixed point quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds, where quicklatex.com-ada3765a264ac03a253ee0ccbe61f602_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds is the distance of the particle from quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds. The particle starts from rest at a distance quicklatex.com-fc85ef309591bf8b549446f3ebd0b450_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds from quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds. Show that the velocity of the particle tends to a limit quicklatex.com-f557b2de47d3ccc8999c2430989f0633_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds.

Question 9

(a) Two particles quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds are moving along two perpendicular lines towards a point quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds with constant velocities of quicklatex.com-06ad4c23e0f9d82dffea8f5855a9f4b5_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds m/s and quicklatex.com-e37a7ce3683aa7c32967f8f4105807da_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds m/s respectively. When quicklatex.com-cba4133f939edee31a8ce51d790a9cd0_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds is quicklatex.com-ed5decd492fdc6648538222379ceaf27_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds metres from quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds, quicklatex.com-eaf6d3ddf3d9ff0d18eb3da055c8c94a_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds is quicklatex.com-2dda138cd42bede9cb97214fc5c8a205_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds metres from quicklatex.com-5b090119e833ac90162777d07e3fe243_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds. Find the distance between them when they are nearest to each other.

(b) State the Principle of Archimedes.

(c) A uniform circular cylinder of height quicklatex.com-63ab7de62920c09a3246a8ce084ab3ce_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and relative density quicklatex.com-273ac051ff0a53582365352ee5b6950d_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds floats with its axis vertical in a liquid of relative density quicklatex.com-d66dbaeb0eebc210a255b3fd356eacd0_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds.

(i) Find the length of the axis of the cylinder immersed.

(ii) The cylinder is depressed vertically a further small distance quicklatex.com-ada3765a264ac03a253ee0ccbe61f602_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds and release. Show that it will preform simple harmonic motion, and find the period.

Question 10

(a) A portion in the shape of an equilateral triangle is removed from a circular lamina of radius quicklatex.com-95d7c225dd31ad7d6dd5fb9f0980b531_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds. A vertex of the triangle was at the centre of the lamina and the sides of the triangle are of length quicklatex.com-95d7c225dd31ad7d6dd5fb9f0980b531_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds. Find the position of the centre of gravity of the remainder.

(b) A train of mass quicklatex.com-f1f207cf5d3c4f0c0d76a93586bcd29b_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds tonnes is maintaining a steady speed of quicklatex.com-739f6781b65065fc445d5f13b544d6b2_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds m/s up an incline of quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds in quicklatex.com-bd7202b6cf8beeda1b46bb2799ac945c_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds against frictional forces amounting to quicklatex.com-cbbca562b8a27132c102a81b44b1362d_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds kN. Calculate the power at which the engine is working. (quicklatex.com-d39c7a34226b6a7fc7b5d3ae51b6b5e4_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds tonne = quicklatex.com-832988d7b85b3784b072284b63fdfa60_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds kg).

(c) A corner on a level track has a radius of quicklatex.com-4fbb80c3d7c3c9bdfaf780287e19f597_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds m. Calculate the maximum speed at which a cyclist could take the corner if the coefficient of friction were quicklatex.com-a5990b654956436786b5311c7aada3b3_l3 | Leaving Cert Applied Maths Higher Level 1978 | Maths Grinds.


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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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