# Skill Builder

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### Interpreting Vectors

###### What to Do

Read about each vector operation, and study the steps. Then solve the Practice Problems that follow.

The steps in the graphical method for adding vectors are given in the table below. In the example, vectors and are added together to give the vector sum . The symbol is often used to represent the resultant vector.

Graphical Vector Subtraction (=÷)

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### Interpreting Vectors(continued)

###### Practice Problems

1. A small airplane flies with a heading of [N45W] from Medicine Hat to Red Deer, a distance of 333 km. The airplane then flies with a heading of [N65E] from Red Deer to Lloydminster, a distance of 281 km. What distance did the airplane fly? What is the airplane’s total displacement for the trip? (Hint: When you work with large displacements, create a scale. For example, you could let 1.00 cm on a graph represent 100 km on a map. Here 333 km on the map would then be represented by 3.33 cm on the graph. When you have measured your resultant vector, use the scale to convert the measurement back to kilometres.)

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2. A swimmer swims 35 m directly north from the shore of a lake to a small island. She then swims 42 m[E24S] to another point on the shore. What distance did the smimmer swim? What is her total displacement? What is her displacement from the point where she landed on the shore to the point from which she started swimming? If she walks back to the point from which she started swimming, what is her total displacement for swimming and walking?

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### Interpreting Vectors(continued)

3. A little dog starts swimming directly north across a river with a speed of 1.8 m/s. The river is flowing directly east with a speed of 0.72 m/s. If the river current carries the dog east as it is swimming north, what is the dog’s velocity relative to the point where it started swimming?

###### Subtracting Vectors Graphically

Some important equations of motion require you to subtract vectors. To do this, you need to know how to draw a negative vector. First draw the positive vector, as shown in the following diagram. Then draw a line that is parallel to the positive vector and exactly the same length. Finally, add the arrow in the opposite direction.

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### Interpreting Vectors(continued)

The steps in the graphical method for subtracting vectors are given in the table below. In the example, vector is subtracted from vector.

Graphical Vector Subtraction (=–)

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### Interpreting Vectors(continued)

###### Practice Problems

1. Rocky Mountain House is at position 159 km[N24W] relative to Calgary. Coronation is at position 215 km[N57E] relative to Calgary. What is the displacement from Rocky Mountain House to Coronation?

2. Joshua’s home is located 1.3 km[W15N] of the high school. Erin’s home is located 2.6 km[N23E] of the high school. What is the displacement from Joshua’s home to Erin’s home?

3. When riding in a car, you look at a compass and the speedometer and see that the car is travelling with a velocity of 85 km/h[E36S]. A while later, you check again and see that the car’s velocity is 55 km/h[E65S]. What is the change in the car’s velocity?