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## Quiz of the Month (September 2005)

### Hector C. Parr

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#### SOLUTION TO LAST MONTH'S QUIZ

1. Horizontal straight line of length 4 ft.
2. Quarter of ellipse, with semi-major axis = 6 ft and semi-minor axis = 2 ft.
3. 7.5 kg.
Notes.
 1. Take F as origin, x-axis vertically downwards, y-axis horizontally to right. Then it is easily seen that point E is at x = 0, y = 4sinq. As q varies from 0 to 90o, y varies from 0 to 4. 2. Point A is at x = 6cosq, y = -2sinq. This is the parametric equation of an ellipse. ```3. Take moments about P. Forces f and g both pass through P and make no contribution. 2w * 4sinq = 20 * 3sinq So w = 7.5 (w = 7.5 at all positions between q = 0o and q = 90o, but is indeterminate at either extreme.)```

#### THIS MONTH'S QUIZ

Ships B and C are both crossing the equator. Ship A is due North of B. The bearing of C from A is S45oE, and the bearing of A from C is N40oW, both bearings measured along the great circle through A and C. The positions of the ships are plotted on a spherical globe of radius 10 cm, and three great circles are drawn, one through A and B, one through B and C, and one through C and A.

1. How many points of intersection are there on the globe between pairs of great circles?

2. Into how many distinct areas is the surface of the globe divided by the great circles?

3. Find the area of triangle ABC on the globe.

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