# Leaving Certificate Examination 1956 Honours Applied Mathematics

#### Question 1

A warship is travelling on a course East of North. To an observer on a liner travelling due East at knots the warship appears to be moving due North. Find the speed of the warship.

In what direction should the warship travel at that speed so that it would appear to the observe to be moving North-Eastwards?

#### Question 2

is an equilateral triangle. Forces of , , lb. wt act along the lines , , respectively. Find the magnitude of the their resultant.

Show that the line of action of their resultant cuts and internally and externally, and find the angle which it makes with produced.

#### Question 3

A uniform ladder is feet long and weighs lb. It rests with one end in contact with a rough horizontal plane (coefficient of friction ) and the other end in contact with a rough vertical wall (coefficient of friction ). If the bottom of the ladder is feet out from the wall, how far can a man who weighs 6330^\circ322\frac{1}{2}t_12t_2t_1t_22ABCDEABE4BCDEBC=1CDALMAL=AM=2CD18300v2\frac{3}{4}v10C15BC20\sqrt{2}hBh=6hxt

ABCDAD=6AB=5CD=11\hat{BAC}=\hat{CDA}=90^\circADADxBx62.5$ lb.]

**Citation:**

**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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