Exploring Vectors
Bundesliga Vectors
Name _____________________
Before drawing vectors…
 Determine the conversion factor for the 100 km scale (1 cm = ??? km) for each of the two maps.
 Read through the Bundesliga Schedule and make a list the locations for all away games that remain.
Assignment I
The starting position (initial position) is your home city. Draw a vector from your home city to the next away game, and then draw a vector from this location to the location of the next away game. Continue drawing vectors until you are at the location of the last away game. This is your final position.
Do the following:
 Find the total distance traveled
 Find the distance and direction for individual vectors from city to city
(distance and direction , 145 km at 40° North of East, for example)
 Draw the resultant for displacement from starting point to end point. Label the resultant vector and highlight it.
Record: total distance ________________ displacement _________________
Assignment II
Draw the following vectors from your team’s home city
125 km north, then 245 km east, then 250 km at 40 degrees west of north and then 100 km south. What is the resultant? Where are you?

Assignment III
From your team’s home city, draw the vectors representing the following air travel:
Mainz, Frankfurt, Leverkusen, Dusseldorf, Monchengladbach, Dortmund, Schalke
430 km/h for 1.3 hours at 35 degrees North of East, then 350 km/h west for 0.50 hr. Draw a final vector to Hamburg. What is the distance and direction to
Hamburg? How long would it take to fly back to your home team’s city at 350 km/h?
Hamburg, Bremen, Wolfsburg, Hannover
430 km/h for 1.1 hours at 50 degrees South of East, then 350 km/h west for 0.50 hr. Draw a final vector to Hamburg. What is the distance and direction to
Hamburg? How long would it take to fly back to your home team’s city at 350 km/h?
Hoffenheim, Stuttgart, Nurnberg, Greuther Furth, Augsburg, Munchen, Freiburg
430 km/h for 1.3 hours at 70 degrees North of East, then 350 km/h west for 0.50 hr. Draw a final vector to Hamburg. What is the distance and direction to
Hamburg? How long would it take to fly back to your home team’s city at 350 km/h?
Assignment IV
(Use Map 2)
Draw one vector representing displacement from Hamburg to Berlin and another from Berlin to Ulm.
Using the Pythagorean Theorem, determine the displacement from Ulm to
Hamburg (distance) and measure the angle.
Find the angle using the equation angle of theta = tan -1 (opp/adj)

Traveling Determining location using vectors
The sports network that covers the Bundesliga games selects one key match on Saturday to set up a temporary studio in the home team’s stadium parking lot. Using the information that follows, determine the location of each of the games spanning a sixweek period and describe the journey.
Studio Headquarters are in Berlin
Week 1 Hamburg (schalke
Week 2 Bremen (Dortmund)
Week 3
Week 4
Nurnberg (stutt)
Munchen
Week 5
Week 6
Freiburg
Mainz
C. Finding the resultant representing average speed and displacement
You are good young player who plays for a third league team in Stuttgart. Two different teams, Dortmund (BVB) and Berlin (BSC) are interested in signing you to a contract.
Your schedule is as follows: travel early by plane to Dortmund on Monday, then to
Berlin on Tuesday, and return to Stuttgart on Wednesday.
Draw and determine the resultant representing average air speed and compass direction given the following information:
Flight time from Stuttgart to Dortmund (1 hr 23 min)
Flight time from Dortmund to Berlin (1hr 41 min)
What is the displacement?