Assignment 3 Name: Key Average = 8.8

Don=t feel obligated to fit your answers into the spaces below each question!

1. Sally is strolling through a forest and notices a Ponderosa Pine that seems to tower over all the other nearby trees. As she stares at the tree, she begins to wonder about the height of the tree. The more she stares, the more fascinated she becomes about the tree=s imposing height. Then Sally realizes that she can Ameasure@ the height of the tree by measuring the length of her shadow. Explain, with a simple diagram, how she can do that?

The sun casts a shadow of the Ponderosa Pine and also casts a shadow of Sally. The ratio of Sally’s height to the length of Sally’s shadow is the same as the ratio of the height of the Ponderosa pine to its shadow.

2. Suppose Sally is 5 feet tall and her shadow on that day in the forest was 3 feet long. When Sally paced off the length of the Ponderosa Pine=s shadow she got about 90 feet. How tall was the tree?

Using the ratio described in 1,

(5 feet)/(3 feet) = (Height of Tree)/(90 feet) à the height of the Ponderosa is 150 feet.

3. Eratosthenes calculated the size of earth sometime around 250 B.C.. Explain in detail the assumptions he had to make about earth and sun to validate his method for deriving the size of earth. In particular, why was it so important that Eratosthenes knew that the sun was directly overhead on a certain day in Syene, a town south of Alexandria, his home in Egypt?

Erastothenes assumed that sun was far enough from earth that the rays of light hitting earth were all parallel. By knowing that the light was able to reach the bottom of the well in Syene, allowed Erastothenes to deduce that rays of light from the sun were going straight toward the center of earth on that particular day. Then by measuring the length of the shadow of a vertical stick at Alexandria, he was able to figure out the angle between Syene and Alexandria. Knowing the angle and the distance between Alexandria and Syene allowed him to find the circumference of earth,

Angle between them)/(360^o) = (Distance between them)/(Circumference of earth)

It was important that Erastothenes knew that Alexandria was due north of Syene so that the distance between them was the correct distance to use in the above ratio.

4. Read Chapter 1, The Principle of Relativity, in the text for Monday. I always find it useful to read the introduction to textbooks to get a better idea of who the author is writing for and why the author thinks we, the readers, ought to read his/her book instead of the zillions of other books on the same topic.