PowerPoint Presentation vectors



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vectors

VECTORS

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
  • 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

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?

  • 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

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

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

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