Chapter 3: Vectors

Vector Notation

v = speed

v (or v )= velocity

Graphical Addition of VectorsA bird flies 100 m due east, then 200 m 45o north

of west. Draw and measure the net displacement.

Tail-to-Tip Method

Correct method

tail

tip

Resultant

A student drives her car• North of 30 km/hr for 1 hour• East at 60 km/hr for 2 hours• North at 50 km/hr for 1 hourDetermine the net displacement

Vector Resolution

A car travels 500 km at an angle 30o north of east. Calculate its x and y displacement.

30o

500 m

East

North

Vector Resolution: Trigonometry

sin = opposite = o

hypotenuse h

cos = adjacent = a

hypotenuse h

tan = opposite = o

adjacent a

h

a

o

A mailman travels 300 m at an angle of 25o N of E, then 100 m at an angle 50o N of E. Calculate the total (resultant) displacement.

25o

B=100 m

East

North

A=300 m

50o

A student walks 100 m at an angle 20o south of west. He then walks 40 m due north, then 65 m at an angle of 35o north of west. How far is he from the starting point?

A mail carrier drives 22.0 km north. She then drives 47.0 km in a direction 60.0o S of E. What is her displacement from the post office?

(Ans: 30.0 km, -38.5o)

A plan travels due east for 620 km, 65o S of E for 440 km, and then 53o S of W for 550 km. What is the displacement from the airport?

(Ans: 960 km, -51o)