PowerPoint Presentation vectors

VECTORS

• Pre-AP Physics

SCALAR

• A SCALAR quantity
• is any quantity in
• physics that has
• MAGNITUDE ONLY

• Number value
• with units

Scalar Example	Magnitude
Speed	35 m/s
Distance	25 meters
Age	16 years

VECTOR

• A VECTOR quantity
• is any quantity in
• physics that has
• BOTH MAGNITUDE
• and DIRECTION

Vector Example	Magnitude and Direction
Velocity	35 m/s, North
Acceleration	10 m/s2, South
Displacement	20 m, East

• Vector quantities can be identified by bold type with an arrow above the symbol.
• V = 23 m/s NE

• Vectors are represented by drawing arrows

• The length and direction of a vector should be drawn to a reasonable scale size and show its magnitude

• 20 km

• 10 km

VECTOR APPLICATION

• ADDITION: When two (2) vectors point in the SAME direction, simply add them together.
• When vectors are added together they should be drawn head to tail to determine the resultant or sum vector.
• The resultant goes from tail of A to head of B.

Let’s Practice

• A man walks 46.5 m east, then another 20 m east.
• Calculate his displacement relative to where he started.

• 66.5 m, E

• 46.5 m, E

• +

• 20 m, E

VECTOR APPLICATION

• SUBTRACTION: When two (2) vectors point in the OPPOSITE direction,
• simply subtract them.

Let’s Practice some more….

• A man walks 46.5 m east, then another 20 m west. Calculate his displacement relative to where he started.

• 26.5 m, E

• 46.5 m, E

• -

• 20 m, W

Graphical Method

• Aligning vectors head to tail and then drawing the resultant from the tail
• of the first to the
• head of the last.

Graphical Vector Addition A + B

• Step 1 – Draw a start point
• Step 2 – Decide on a scale
• Step 3 – Draw Vector A to scale
• Step 4 – Vector B’s tail begin at Vector A’s head. Draw Vector B to scale.
• Step 5 – Draw a line connecting the initial start point to the head of B. This is the resultant.

NON CO-LINEAR VECTORS

• When two (2) vectors are PERPENDICULAR to each other, you must use the PYTHAGOREAN THEOREM

Let’s Practice

• A man travels 120 km east then 160 km north. Calculate his resultant displacement.

• VERTICAL
• COMPONENT

• FINISH

• 120 km, E

• 160 km, N

• the hypotenuse is
• called the RESULTANT

• HORIZONTAL COMPONENT

WHAT ABOUT DIRECTION?

• In the example, DISPLACEMENT is asked for and since it is a VECTOR quantity,
• we need to report its direction.

• N

• S

• E

• W

• N of E

• E of N

• S of W

• W of S

• N of W

• W of N

• S of E

• E of S

• NOTE: When drawing a right triangle that conveys some type of motion, you MUST draw your components HEAD TO TOE.

• N of E

Directions

• There is a difference between Northwest and West of North

NEED A VALUE – ANGLE!

• Just putting N of E is not good enough (how far north of east ?).
• We need to find a numeric value for the direction.

• 160 km, N

• 120 km, E

• To find the value of the angle we use a Trig function called TANGENT.

• N of E

• 

• 200 km

• So the COMPLETE final answer is : 200 km, 53.1 degrees North of East

What are your missing components?

• Suppose a person walked 65 m, 25 degrees East of North. What were his horizontal and vertical components?

• 65 m

• 25˚

• H.C. = ?

• V.C = ?

• The goal: ALWAYS MAKE A RIGHT TRIANGLE!
• To solve for components, we often use the trig functions sine and cosine.

Example

• A bear, searching for food wanders 35 meters east then 20 meters north. Frustrated, he wanders another 12 meters west then 6 meters south. Calculate the bear's displacement.

• 35 m, E

• 20 m, N

• 12 m, W

• 6 m, S

• -

• =

• 23 m, E

• -

• =

• 14 m, N

• 23 m, E

• 14 m, N

• The Final Answer: 26.93 m, 31.3 degrees NORTH of EAST

• R

• 

Example

• A boat moves with a velocity of 15 m/s, N in a river which flows with a velocity of 8.0 m/s, west. Calculate the boat's resultant velocity with respect to due north.

• 15 m/s, N

• 8.0 m/s, W

• Rv

• 

• The Final Answer : 17 m/s, @ 28.1 degrees West of North

Example

• A plane moves with a velocity of 63.5 m/s at 32 degrees South of East. Calculate the plane's horizontal and vertical velocity components.

• 63.5 m/s

• 32˚

• H.C. =?

• V.C. = ?

Example

• A storm system moves 5000 km due east, then shifts course at 40 degrees North of East for 1500 km. Calculate the storm's resultant displacement.

• 5000 km, E

• 40

• 1500 km

• H.C.

• V.C.

• 5000 km + 1149.1 km = 6149.1 km

• 6149.1 km

• 964.2 km

• R

• 

• The Final Answer: 6224.2 km @ 8.92 degrees, North of East