Objectives: - We will apply vector mathematics to velocity

I will find the x-component and y-component of a velocity vector.

1.  Let’s start today with a riddle: A hunter leaves his base camp one morning and travels one mile due south. He then turns and travels one mile due east. At this point, he sees a bear. Taking the direct route, he travels one mile due north and is back at the base camp. What color is the bear?

2.  Complete the trigonometry worksheet next to the bin

You are flying a kite and have let out 80 m of string. The kite’s angle of elevation relative to the ground is 60 degrees. Assuming the string is stretched straight, how high is the kite above the ground?

Vectors

 Vectors require a magnitude AND direction. ◦  If the direction is in any of the cardinal

directions, you can say:   north, south, east, west, or positive y-direction,

negative y-direction, positive x-direction, negative x-direction

◦  If it is between those four, you must include an angle!

θ

θ

θ

θ

You travel 9 km east, 10 km north, 7 km west and 17 km south. What is your resultant displacement and what direction are you going (answer with an angle)?

You travel 4 km south, 6 km west, 3 km north and 8 km west. What is your resultant and what direction are you going (answer with an angle)?

A plane flies east at 120 m/s through a cross wind of 50 m/s at a right angle (going North). What is the resultant velocity of the plane?

 You can always break up a velocity into the x-component and y-component.

Velocity in the x-direction:

Velocity in the y-direction:

 Polar ◦  (r, θ)

 Cartesian ◦  (x, y)

The positive x- direction is east and the positive y-direction is north. If a raven starts from the origin and flies with a constant velocity of 5 m/s directed 36.9° north of east, 1.  How far East has the raven traveled in 5

minutes? 2.  How far North has the raven traveled in 10

minutes? 3.  What is the total displacement after 15

minutes?

  If a husky starts at the location (-3, -4) and ends at (10, 4) after 10 seconds. What average velocity does the husky have over his journey?

  If a sailboat is traveling with a velocity of 20 m/s pointed 25° north of east, ◦ What component of the velocity is directed

North? ◦ What component of the velocity is directed

East?

  If a sailboat is traveling with a velocity of 20 m/s pointed 60° north of east, ◦ What component of the velocity is directed

North? ◦ What component of the velocity is directed

East?

Sophie is on a train moving West at 60 m/s. She moves towards the back of the train at 6 m/s.

 What is Sophie’s resultant velocity, relative to the ground?

 Ernesto is sailing around the Mediterranean on a yacht. The yacht moving forward, due East at 20 m/s. Ernesto starts from the Starboard side (right side of the boat) and runs at 8 m/s to the Port side (left side of the boat). ◦ Hint: draw a picture

 How fast is Ernesto moving relative to the water?

 Vectors HW 2 worksheet ◦ Answers will be posted on my website after

we complete the example problems in class ◦ The HW quiz will have different numbers. ◦ HW quiz next week.