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

A graphical representation of a Vector is an arrow of Specified length and direction.

50 An algebraic representation of a Vector is a boldface letter with A number and direction.

Like… d = 50m southwest

Two displacement are equal when The two distances and direction Are the same. A resultant vector is equal to the Sum of two or more vectors. R b a

Adding the vectors like on the Board only works if the Vectors are at right angles. Or by using the Pythagorean Theorem… R 2 = A 2 + B 2

If you are adding vectors that Are not at right angles, You have to use the law of Cosines.

R

2

= A

2

+ B

2

- 2ABcosθ

Find the magnitude of the sum Of a 15km displacement and a 25km 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 scalar Number changes its length but Not its direction unless the scalar Is negative. Then, the vector’s Direction is negative.

This fact can be used to subtract Two vectors using the same Method for adding them.

ΔV = V 2 - V 1 ΔV = V 2 + (-V 1 )

An airplane flies due north at 150 km/h with respect to the air. There is a wind blowing at 75 km/h To 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 = a c cos θ = side adjacent to hypotenuse = b c tan θ = side opposite θ side adjacent to θ = a b

By adjusting the trig functions We can find the parts of any Vector.

A A y A x A x = A cos θ A y = 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. A x = 19.9km

A y = 11.5 km

R

2

= R

x 2

+ R

y 2 Tan θ = R x 2 R y 2

A person attempts to measure the height Of a building by walking out a distance of 46.0 m from its base and shined a laser Toward 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 exerted On 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 surfaces In contact. This is why we classify them With the coefficient of friction.

The coefficient of friction is the Ratio of the force of friction To the normal force acting Between two objects.

µ

s

= F

s n

µ

K

= F

k n

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 resting On a plane inclined at 30 above The horizontal. Find the Components of the weight force Parallel and perpendicular The plane.

F gX = 281N F gY = 487N

A 62 kg person on skis is going Down a slope at 37°. The coefficient Of kinetic friction is 0.15. How fast Is the skier going 5 s after Starting from rest?

24 m/s