Exercise 2

Exercise #2: Math, Units and Quantities

(Show calculations & include units)

Due Tuesday, October 6th

(You can also download the Word version of the Exercise#2 Answer Sheet HERE).

(or PDF version HERE)

Purpose: To review and get comfortable with basic math, physical quantities and units.

1. (one point) A map is based on the Universal Transverse Mercator (UTM) reference system, such that locations are specified with Easting (E) and Northing (N) coordinates relative to an origin. Distances are in units of meters (m). If on the map, the coordinates of Beach Town are N384240; E256940, how far is it (in meters and in kilometers (km) to Sand City that has coordinates of N368620; E239200? [Note that N384240 means that Beach Town is 384,240 m (or 384.24 km) north of the UTM origin and E256940 means that it is 256,940 m east of the origin.] [Hint: The Pythagorean theorem is appropriate to use here, since UTM coordinates are essentially Cartesian coordinates]

2. (one point) You are reviewing an aerial photograph to determine forest conditions and need to know how tall a specific tree is. The perfectly straight tree casts a shadow on level ground that is measured to be 220 m.

(a) How tall is the tree if the sun angle (measured from the ground) is 30⁰?
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Hint: Make a drawing of the tower-ground-sun relationship and then use the appropriate trigonometric functions to solve the problems.

(b) What is the solar zenith angle (measured from zenith) if the sun angle is 30 degrees?
____________________

(c) At a different time of day the tree casts a shadow that is 123 m. What was the sun angle at that time of day?
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(d) Mathematically speaking, explain why the approach used to estimate the height of the tree based on its shadow length, would not work for the famous tower of Pisa.

3. (one point) Typically, altitude, elevation and depth are represented by the variable z (where for altitude or elevation z increases going up, for depth decreases (increasingly negative) going down, and is 0 at the ground surface). Temperature is normally represented by the variable T (since t is used to represent time).

Altitude (m)	Temperature (⁰C)
0	20
1000	12
2000	4

a. Write a linear equation (slope-intercept form) that describes the constant linear decrease in temperature with increasing altitude and that fits the data in the table above.

b. Given the linear relationship between altitude (z) and temperature (T). What is the altitude, in meters, when the temperature is -2^°C?

4. (one point) An aerial photograph has a scale of 1:25,000 or 1/25,000. This means that a feature on the ground that is 25,000 cm (equal to 250 m) in length is shown on the photograph as a 1 cm feature.

a. If a road segment is measured to be 2.2 cm on the aerial photograph, what is the actual length of the road segment (on the ground) in cm, m, and km?

b. How long is a football field (from end zone to end zone) on the aerial photograph?

5. (one point) Much of the land in the western US is divided up into square parcels based on the Township and Range land ownership system. A section is a square parcel of land that measures 1 mile on each side. Each section is divided into four quarter sections that are 0.5 mile on each side. If a quarter section wholly contains a circular field (as shown in the figure below) that is irrigated by a central pivot sprinkler system.

circle

a. What is the diameter of this circular field?

b. How long is the central pivot irrigation system?

c. What is the total area of irrigated land in this quarter section?

d. What is the area of land that not irrigated in this quarter section?

6. (one point) Convert the following; make sure you understand why you are using a particular conversion factor – don’t just push calculator or computer buttons that enable conversions.

	From	To
a.	10 kilometers =>	____________ miles
b.	10 kilometers =>	____________ meters
c.	30 square feet =>	____________ square meters
d.	500 cubic meters =>	____________ cubic feet
e.	50 acres =>	____________ hectares
f.	25 miles per hour =>	____________ meters per second

7. (two points). You are given a paper map showing an area of interest to the Grantville Metropolitan Police Department. The map is based on the Universal Transverse Mercator (UTM) reference system, such that locations are specified with Easting (E) and Northing (N) coordinates relative to an origin. Distances are in units of feet (ft). The boundary of the area of interest is identified on the map by three points: P1 (N547.150; E1148.293), P2 (N1558.400; E1148.293), and P3 (N547.150; E1804.462). You need to transfer these points to a map that uses UTM with the distance in units of meters. What are the corresponding coordinates for each of the three points, P1 – P3? What is the area of the shape that the police department is interested in (your answer should be in m²)?

Note:

You should finish this exercise (in paper with detail calculation procedures and answers) and then upload your answer sheets (just the answers) to the Blackboard ( http://blackboard.sdsu.edu ) before the lecture. Submit the paper version in the class (11:00am). We will use the Timestamp on your documents in the Blackboard to check if your assignment is late or not.

(In your upload file, please use this title: [GEOG104-LAB-#-[Your name].doc (or txt or pdf). Please write down your answers in MS Word or WordPAD or other word processing software. Please always save a local backup copy of your own answers.)