Physics 101- Introduction to Mechanics
January 16

Let's consider a evening at the beach.  What happens at sunset?  Would your friend sitting on the balcony of his beachfront apartment (10 stories up), see the sunset at the same time as you (while on the beach)?

Let's label the radius of the earth (r), the difference in height between you on the beach and your friend upstairs (h), the angle formed between the two "horizons" (which is also the same angle betweent he sun's two positions) and a useful distance d.

Write two expressions for d one in terms of r & h and the other in terms of r and q.  Write an expression q for in terms of the time difference between sunsets, t. (Hint: how long does it take for the sun to travel in a full circle?  Can you use this in a ratio with the partial circle (q) shown here?)  Then combine the equations to find r in terms of the time difference between sunsets and the height difference, h.

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 Jeff Phillips phillips@lmu.edu Loyola Marymount University Spring 2002