This is the first real homework set for ES 10. It consists of 6 quickie-type questions each worth 5 points, two longer questions each worth 10 points, and one big question, worth 50 points. The big question will require you to use several of the subjects discussed in Handout 1, which you should also have. This homework assignment is due at the beginning of lecture on 17 January.
If you have problems or questions, please come see me in my office hours or send me an e-mail. My office hours are Monday and Wednesday right after class, from 2:00-3:30 pm, in 1539 Galbraith Hall. I will not hold office hours on 20 January, due to the long Martin Luther King, Jr. holiday. I will try to arrange extra office hours during the week of 20 January to make up for my absence. If you can't make my office hours, or you have a question outside of them, please feel free to send me an e-mail. We can either try to answer the problem via e-mail or we can try to arrange an appointment either down here at SIO, or up on the main campus. My e-mail address is email@example.com
Question 1. Write the following numbers as powers of ten. (5 points)
Question 2. Write the following numbers in ``normal'' notation. (5 points)
Question 3. Do the following problems. (5 points)
Question 4. Write the following numbers in scientific notation. (5 points)
Question 5. Write the following numbers in ``normal'' notation. (5 points)
Question 6. Perform the following calculations. Show your work for credit. (5 points)
Question 7. Show your work for full credit. (10 points)
A cop pulls you over for speeding. He says, ``I clocked your speed at 33.5 m/s. The speed limit here is 29.1 m/s. I'll have to give you a ticket.'' If tickets cost $5 per mph over the speed limit, how much is the fine for this ticket?
Question 8. Show your work for full credit. (10 points)
You've decided to throw a big Super Bowl party to root for the Carolina Panthers. You've decided to get a keg of Sierra Nevada Pale Ale to serve at your party.
Question 9. The Age of the Universe (50 points)
In this problem, you will calculate the age of the universe from a set of numbers I'll give you. I hope it will be fairly interesting, and not just drudgery for you. First, a little background physics will probably be helpful.
Let's say I drive up to Magic Mountain next month to ride some roller coasters. It's roughly 180 miles away up north of LA, for those who don't know. If I drive a nice steady 60 mph (no doubt getting yelled at by everyone else on the road), how long would it take me to get there? You know the answer almost immediately, no doubt, but let's look at it in equation terms.
The relationship between distance, speed, and time is given by
From Equation 2, you will probably see that you can answer my first question easily. Since , all you have to do is divide the distance by the speed, and you get the answer, which in my case is 3 hours. By the way, you probably also noticed that Equation 2 is the equation for a straight line. That means that the relationship between distance and speed is a linear one, and that if you plot a graph with distance as a function of speed, you will see a straight line.
OK, now the problem. Dr. Tauxe has put together a table (Table 1) which gives distances to and speeds of a bunch of distant galaxies. You will use these numbers to make a graph, draw a line on that graph, and thus find the age of the universe.
Actually, if you're sharp, you'll notice that Table 1 doesn't actually contain the distances and speeds, but their logarithms. So you will have to convert these logs back into the original numbers in order to make your graph.
So here's what I want you to do:
Here is what I want you to turn in for this problem.
The table of logarithms, Table 1, is shown below.
Table 1: Logarithms of Retreat Speeds of and Distances to Distant Galaxies