There are two different ways to Represent vectors, Graphically and Algebraically.

There are two different ways toRepresent vectors,

Graphically andAlgebraically

A graphical representation of aVector is an arrow of

Specified length and direction.

An algebraic representation of a Vector is a boldface letter with

A number and direction.

Like… d = 50m southwest

50

Two displacement are equal whenThe two distances and direction

Are the same.

A resultant vector is equal to the Sum of two or more vectors.

a

b

R

Adding the vectors like on the Board only works if the

Vectors are at right angles.

Or by using the PythagoreanTheorem…

R2 = A2 + B2

If you are adding vectors thatAre not at right angles,

You have to use the law ofCosines.

R2 = A2 + B2 - 2ABcosθ

Find the magnitude of the sumOf a 15km displacement and a25km displacement when the Angle between them is 135°.

R = 37 km

A car is driven 125 km due west,Then 65 km due south. What is the

Magnitude of its displacement.

R = 140 km

Multiplying a vector by a scalarNumber changes its length but

Not its direction unless the scalarIs negative. Then, the vector’s

Direction is negative.

This fact can be used to subtractTwo vectors using the same

Method for adding them.

ΔV = V2 - V1

ΔV = V2 + (-V1)

An airplane flies due north at 150 km/h with respect to the air.

There is a wind blowing at 75 km/hTo the east relative to the ground.

What is the plane’s speed with Respect to the ground.

170 km/h

By using the trig functions,You can figure out the components

Of any vector.

We will be dealing with the Trigonometric functions a lot!!

sin θ =side oppositeθ

hypotenuse =ac

cos θ =side adjacent to

hypotenuse =bc

tan θ = side opposite θside adjacent to θ =

ab

By adjusting the trig functionsWe can find the parts of any

Vector.

A

Ax

Ay

Ax = A cos θ

Ay = A sin θ

A bus travels 23.0 km on a Straight road that is 30° north of

East. What are the east and North components of its

Displacement.

Ax = 19.9km Ay = 11.5 km

R2 = Rx2 + Ry

2

Tan θ = Rx

2

Ry2

A person attempts to measure the heightOf a building by walking out a distance of

46.0 m from its base and shined a laserToward the top. They found that the laser

Was at an angle of 39.0°. How tall Is the building?

37.3m

There are two types of friction:Static and Kinetic.

Static friction is the force exertedOn a motionless body by its

Environment to resist An external force.

Kinetic friction is the force Exerted on a moving object.

Friction depends on the surfacesIn contact.

This is why we classify them With the coefficient of friction.

The coefficient of friction is the Ratio of the force of frictionTo the normal force acting

Between two objects.

µs = Fs Fn

µK = Fk

Fn

You push a 25 kg wooden box Across a wooden floor at a

Constant speed of 1 m/s. How Mush force do you exert on

The box?

49 N to the right

An object is in equilibrium when The net force on it is zero.

An equilibrant is a force, that when Added to others, makes the Net force of an object zero.

A trunk weighing 562 N is restingOn a plane inclined at 30 above

The horizontal. Find the Components of the weight force

Parallel and perpendicular The plane.

FgX = 281N FgY = 487N

A 62 kg person on skis is going Down a slope at 37°. The coefficientOf kinetic friction is 0.15. How fast

Is the skier going 5 s after Starting from rest?

24 m/s