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Quiz of the Month (August 2004)

Hector C. Parr

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SOLUTION TO LAST MONTH'S QUIZ

    1.  1/4
    2.  1/2
    3.  0.05365 (or 1/4 - PI/16 )

Notes

The illustration shows one square of the board, and the coloured areas show the regions within which the centre of the coin must land for the coin to cover parts of 1, 2 or 3 squares respectively. The required probabilities are proportional to the relative areas, and are easily calculated.

THIS MONTH'S QUIZ

(Consider the earth to be a perfect sphere with radius 6400 km.)

1. A geo-stationary satellite is positioned directly over a point on the equator at a height of 36,000 km above the earth's surface. What is the latitude of the most northerly point on the earth's surface from which the satellite can be seen?

2. From what fraction of the earth's surface can the satellite be seen?

3. There are, in fact, three such satellites positioned at the vertices of an equilateral triangle. What is the latitude of the most northerly point from which two of these satellites are visible?

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© Hector C. Parr (2004)

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