Chapter 3 ReviewTwo-Dimensional Motion

Essential Question(s):

How can we describe the motion of an object in two dimensions using the one-dimensional concepts of displacement, velocity, and acceleration?

Upcoming Schedule

Today: 3.1-3.2 Vectors and Trigonometry Tomorrow: 3.3-3.4 Projectile and Relative

Motion Monday: 4.1-4.3 Newton’s Laws Tuesday: 4.4 Everyday Forces (friction and

inclined planes!) Wednesday: Last day of review! Thursday: Semester Exam.

Objective(s):

Add vectors graphically and algebraically. Determine components of vectors. Calculate displacement, velocity and

acceleration of objects moving in two dimensions.

Describe the motion of objects in different frames of reference.

Agenda: Have a half sheet of paper! Thursday:

Vectors and Scalars Adding and Subtracting Vectors Graphically Determining Algebraic Components of Vectors Adding and Subtracting Vectors Algebraically

Friday Projectile Motion

launched horizontally launched at an angle

Relative Motion

What are Vectors?

Vector: a physical quantity that has both a magnitude and a direction. Example: Velocity 22 m/s North

Scalar: a physical quantity that can be completely described by its magnitude (number and units). Example: Speed 22 m/s

How to Add Vectors Vectors may be

moved parallel to themselves in any diagram.

Vectors can be added in any order.

To subtract a vector, add its opposite.

Adding Perpendicular Vectors: Magnitude

Use the Pythagorean Theorem

For example: use the Pythagorean theorem to find the magnitude of the displacement given its horizontal and vertical components

Adding Perpendicular Vectors: Direction

Use the inverse tangent function of your calculator

Remember: This only tells you the angle, not the direction relative to North or the horizon

Your Turn: Adding Perpendicular Vectors

A student walks 4.0 m South and then 9.0 m East. What is the student’s displacement vector?

Magnitude:

d2 = 9.02 + 4.02 = 81.0 + 16.0d2 = 97.0d = √97.0 = 9.8 m

Direction:

tan θ = 9.0/4.0 = 2.25θ = tan-1 (2.25) θ = 66°

Displacement vector: 9.8 m at 66° E of S

Resolving Vectors into Components

In other words Opp = hyp * sin θ

Adj = hyp * cos θ

Your Turn: Resolving Vectors into Components

Find the component velocities of a helicopter traveling at 95 km/h at an angle of 35° to the ground.

Adding Non-Perpendicular Vectors

1. Resolve all vectors into horizontal and vertical components.

2. Add components to find total horizontal and vertical components of resultant.

3. Calculate magnitude and direction of resultant.

Try adding 40.0 m at 20.0° below the horizontal and 100.0 m at 35° above the horizontal.

Homework

p 97 Section Review #2 (adding perpendicular vectors) #3 (finding vector components) #4 (adding non-perpendicular vectors)