Geographic Information Science and Spatial Reasoning

(GEOG 104)  (A General Education [GE]  Course)  Spring 2018

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Geographic Information Science and Spatial Reasoning

(GEOG 104)  (A General Education [GE]  Course)  Fall 2015

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Web-based Exercise #2:

Quantitative Reasoning

 

Estimated time: 1.5 hour

Grading:  8 points total (ONE point for each question).

 

Due Day: Feb 26 at the beginning of lecture (9:30am). You should upload your lab answers to the Blackboard ( http://blackboard.sdsu.edu  )  before the lecture and submit a paper print-out version in the class.  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.)

 

If you don't have Internet access, you can use our SAL lab (Storm Hall 338, third floor) on every Friday morning from 11:00am to 12:00pm.

 

Contents:

 

Exercise #1:  Math, Units and Quantities

(Show calculations & include units)

Due Tuesday, February 10

 

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

 

1.  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.  A tall radio tower casts a shadow on level ground that is measured to be 220 m.

 (a) How tall is the tower if the sun angle (measured from the ground) is 300?

( 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 radio tower casts a shadow that is 123 m.  What was the sun angle at that time of day?

           

 

 

            (d) Mathematically speaking, explain why the approach used to estimate the height of the
                 tower based on its shadow length, would not work for the famous tower of Pisa.

 

 

3. 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 that this relationship is linear (i.e., that temperature decreases at a constant rate), express the relationship as a differential equation (i.e., using the derivative symbol from calculus).

 

 

 

 

 

4.   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.  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.                                Central pivot irrigation

 


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.   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

 

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Note:

You should upload your lab answers to the Blackboard ( http://blackboard.sdsu.edu  )  before the lecture and submit a paper print-out version in the class.  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.)

 

If you don't have Internet access, you can use our SAL lab (Storm Hall 338, third floor) on every Friday morning from 11:00am to 12:00pm.

 

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This web site is hosted on MAP.SDSU.EDU
and Geography Department.

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This web site is hosted on MAP.SDSU.EDU
and Geography Department.