adding vectors algebraically

3.1 Introduction to Vectors

Page 82

Section Objectives

Distinguish between a vector and a scalar. Add and subtract vectors by using the

graphical method.

Scalar Quantities

Scalars can be completely described by magnitude (size)

Scalars can be added algebraically They are expressed as positive or negative

numbers and a unit examples include: mass, electric charge,

distance, speed, energy

Vector Quantities

Vectors need both a magnitude and a direction to describe them (also a point of application)

They need to be added, subtracted and multiplied in a special way

Examples :- velocity, weight, acceleration, displacement, momentum, force

Distinguish between a scalar and a vector.

The acceleration of a plane as it takes off. The duration of a flight. The displacement of the flight The amount of fuel required for the flight. The force acting on the plane in the form of

air resistance.

3.2 Vector Operations

Page 86

Section Objectives

Calculate the magnitude and direction of a resultant vector.

Resolve vectors into components. Add vectors that are not perpendicular.

Terminology

Two or more vectors can be combined together to form a resultant

A vector that does not lie along the x or y-axis may be resolved into its components


Draw 20 south of west.

Draw 20 west of south.


Use the Pythagorean Theorem to find the magnitude of the resultant.


Use SOHCAHTOA to find the direction of the resultant.

Resolve vectors into components.

Every vector can be resolved into its x and y components using trigonometry.

If a vector is located on the x or y axis, then the other component of that vector is zero.

Resolve vectors into components.

Add vectors that are NOT perpendicular

If the original displacement vectors do not form a right triangle 1. Resolve each vector into its x- and y-

components 2. Find the sum of the x- and y-components 3. Use the Pythagorean Theorem to find the

magnitude of the resultant 4. Use the tangent function to find the direction of

the resultant

Adding non-perpendicular vectors

Practice #1

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 between the base camp and the tower.

Check you work!

Page 89

1. a) 23 km

b) 17 to the east

2. 45.6 m at 9.5° east of north

3. 15.7 m at 22° to the side of downfield

4. 1.8 m at 49° below the horizontal

Check your work!

Page 92

1. 95 km/h

2. 44 km/h

3. x=21 m/s, y=5.7 m/s

4. x=0 m , y=5m

Practice #1

A bullet travels 85 m before it glances off a rock. It ricochets off the rock and travels for an additional 64 m at an angle of 36 degrees to the right of its previous forward motion. What is the displacement of the bullet during this path.

Make physics YOUR

business. Try

problems 1-4 on pages

94.

Dr. Miller says: Time for some practice! Try pages 89 & 92.

Check your work!

Page 94

1. 49 m at 7.3° to the right of downfield2. 7.5 km at 26° above the horizontal3. 13.0 m at 57° north of east4. 171 km at 34° east of north

Problem 3C

1. 216.5 m at 30.0 north of east

2. 2.89 Χ 104 m at 21.7 above the horizontal

4. 1320 km at 3.5 east of north

5. 221 km at 11.2 north of east

Add and subtract vectors by using the graphical method.

Multiply and divide vectors by scalars.

Multiplying or dividing vectors by scalars results in _________________.

You are in a cab traveling 25 mph east. You tell the cab driver to drive twice as fast. Your new velocity is ____________________.

You are in a cab traveling 25 mph east. You tell the cab driver to drive twice as fast in the opposite direction. Your new velocity is ________________.


T / F Vectors can be added in any order. T / F Vectors can be moved parallel to

themselves in diagrams. Let’s see:

http://www.physicsclassroom.com/mmedia/vectors/ao.cfm


http://www.physicsclassroom.com/Class/vectors/u3l1b.cfm

adding vectors algebraically

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