Physics 109N Homework #3

Due Tuesday September 24, 1996

Out of sight?

1. If you stand on a beach, and the ocean is fairly peaceful, the distance you can see-the horizon-relates to the curvature of the earth. H and T denote your head and toes as you stand on the beach. A is the furthest you can see the surface of the water. C is the center of the earth. AH is a tangent to the earth's surface at A (right?), so CAH is a right angled triangle. Apply Pythagoras' theorem to this triangle, and see if you can figure out how far away the horizon is-that is, assume HT is one-thousandth of a mile (is it?) take the earth's diameter to be 7,900 miles, and figure out just how far you can see, before the earth's curvature stops you.

Equinox

2. On Monday, September 23, the sun will set exactly twelve hours after it rises in Charlottesville. For what other parts of the world will that also be true? Where in the world will the sun be exactly overhead at midday on Monday? Describe the motion of the sun as seen in the sky from the north pole on that day. What is the angle between the vertical and a pencil pointing directly at the sun at midday in Charlottesville on Saturday? What is the latitude of Charlottesville? Are these angles related?

Wise guys

3. After reviewing the notes, and any other material you wish, decide who you think are the twelve Greek scientist/mathematicians who contributed most to our understanding of the universe (not counting medical or theological contributions). Construct a "time-line", by which I mean plot out on a piece of paper, with a scale from 600 BC to 200 AD, say, showing each one's lifetime with a line. Put the person's name by each line, and a few words about what they did.

Easy as pi

4. Check your understanding of Archimedes' calculation of pi by finding what lower bound on the value of pi you can discover by inscribing first a square, then a regular octagon, in a circle.