Vectors

Ch. 2 Sec 1

Section Objectivies

Distinguish between a scaler and a vector.

Add and subtract vectors by using the graphical method.

Multiply and Divide vectors by scalers.

Scalers and Vectors

A scaler is a quantity that has a magnitude but no direction. Ex. Speed, volume, number of pages in a

bookA vector is a physical quantity that has

both a direction and magnitude. Ex. Velocity and Acceleration

A resultant vector is the addition of two vectors.

Adding Vectors Vectors can be

added graphically. A student walks from

his house to his friend’s house (a), then from his friend’s house to the school (b). The student’s resultant displacement (c) can be found by using a ruler and a protractor.

Triangle Method Vectors can be moved parallel to themselves

in a diagram. Thus, you can draw one vector with its tail

starting at the tip of the other as long as the size and direction of each vector do not change.

The resultant vector can then be drawn from the tail of the first vector to the tip of the last vector.

Show Clip 580

Properties of Vectors

Vectors can be added in any order.To subtract a vector add its opposite.Multiplying or dividing vectors by

scalers results in vectors.

Subtraction of Vectors

Show 581

Multiplication of Vectors

Show 582

Homework

P 85 1- 5

P 108 1 – 9, 11, 12

Vectors Part II

Chapter 3 Section 2

Section Objectives

Identify appropriate coordinate systems for solving problems with vectors

Apply Pythagorean theorem and tangent function to calculate the magnitude and direction of a resultant vector.

Resolve vectors into components using sine and cosine functions

Add vectors that are not perpendicular

Determining resultant Magnitude and DirectionIn section one, the magnitude and

direction were found graphically. This is very time consuming and not very

accurate. A simpler method uses Pythagorean

theorem and the tangent function.

Use the Pythagorean Theorem to find magnitude of the resultant If a tourist was climbing a

pyramid in egypt. The tourist knows the height and width of the pyramid and would like to know the distance covered in the climb from the bottom to the top.

c = the distance covered b = The width of the pyramid a = The height of the

pyramid.

Use the tangent Function to find the direction of the resultant To find the direction

remember to take the inverse tangent.

Sample Problem A An archaeologist climbs the Great Pyramid in Giza,

Egypt. The pyramid’s height is 136 m and its width is 2.3 x 102 m. What is the magnitude and direction of the displacement of the aechaeologist after she climbs from the bottom of the pyramid to the top.

First draw a picture. Given

h = 136 w = 2.3 x 102 m

Find magnitude and angle

Vector Components

The horizontal and vertical values for a vector are called its components. x component is parallel to the x-axis y component is parallel to the y-axis

To find the components use the sine and the cosine. cos θ = adj/hyp; usually x sin θ = opp/hyp; usually y

Sample Problem

Find the components of the velocity of a helicopter traveling 95 km/hr at an angle of 35° to the ground. Given

V = 95 km/hΘ = 35 °

Unknownvx = ?Vy = ?

Clip 585

Sample problem A hiker walks 27.0 km

from her base camp at 35° south of east. The next day, she walks 41.0 km in a direction 65° north of east and discovers a forest ranger’s tower. Find the magnitude and direction of her resultant displacement

Homework Page 89

1-4 Page 92

1-4 Page 94

1-4 Section Review 2, 3

Page 109 14,15, 21 - 26

Chapter 3Section 3.3

Projectile Motion

Section Objectives

Recognize examples of projectile motion.

Describe the path of a projectile as a parabola.

Resolve vectors into their components and apply the kinematic equations to solve problems involving projectile motion.

Projectiles Objects that are thrown or launched into the air and

are subject to gravity are called projectiles.

Projectile motion is the curved path that an object follows when thrown, launched,or otherwise projected near the surface of Earth.

If air resistance is disregarded, projectiles follow parabolic trajectories.

Projectiles

Projectile motion is free fall with an initial horizontal velocity.

The yellow ball is given an initial horizontal velocity and the red ball is dropped. Both balls fall at the same rate. In this book, the horizontal velocity of a

projectile will be considered constant. This would not be the case if we

accounted for air resistance.

Kinematic Equations for Projectiles In the vertical direction, the acceleration ay will

equal –g (–9.81 m/s2) because the only vertical component of acceleration is free-fall acceleration.

In the horizontal direction, the acceleration is zero, so the velocity is constant.

Classwork

P101 1 S.R.P 109 27 - 30