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5 minutes 15 mph North 20 miles East 25 Dollars 15 lbs downward 6 knotts at 15° East of North

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5 minutes 15 mph North 20 miles East 25 Dollars 15 lbs downward 6 knotts at 15° East of North 23 cm3. Scalars and Vectors. Scalars and Vectors. Scalars. Vectors. Vector = size AND direction Ex: displacement, velocity, acceleration Cannot use normal arithmetic. Ex:

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Presentation Transcript
slide1

5 minutes

15 mph North

20 miles East

25 Dollars

15 lbs downward

6 knotts at 15° East of North

23 cm3

scalars and vectors1
Scalars and Vectors

Scalars

Vectors

  • Vector = size AND direction
  • Ex: displacement, velocity, acceleration
  • Cannot use normal arithmetic.
  • Ex:

3mi + 2mi = 1mi

3mi + 2mi = 5 mi

3mi + 2mi = 3.6mi

Scalar = magnitude or quantity (size)

Ex: mass, energy, money, distance

Normal Number

Can add, subtract, multiply, etc normally.

Ex:

3mi + 2mi = 5mi!

notation of vectors symbol
Notation of Vectors (symbol)

Angle of vector from positive x-axis

Name of vector

Magnitude of Vector

slide5

2.3

45°

adding vectors graphically
Adding Vectors Graphically

Remember: Head to tail

if c is a vector then a and b are the vertical and horizontal components
If C is a vector, then A and B are the vertical and horizontal components

However, we are going to use different notations for B and A…..

however we are going to use different names for a and b
However, we are going to use different names for A and B

θ

What are the equations for Cx and Cy?

vector addition
Vector Addition
  • Resultant vector
  • Not the sum of the magnitudes
  • Vectors add head-to-tail
  • x-components add to givex-component of resultant
  • y-components add to givey-component of resultant
adding vectors by components1
Adding Vectors by Components

B

A

Transform vectors so they are head-to-tail.

adding vectors by components2
Adding Vectors by Components

Bx

By

B

A

Ay

Ax

Draw components of each vector...

adding vectors by components3
Adding Vectors by Components

B

A

By

Ay

Ax

Bx

Add components as collinear vectors!

adding vectors by components4
Adding Vectors by Components

B

A

By

Ay

Ry

Ax

Bx

Rx

Draw resultants in each direction...

adding vectors by components5
Adding Vectors by Components

B

A

R

Ry

q

Rx

Combine components of answer using the head to tail method...

adding vectors by components6
Adding Vectors by Components

Use the Pythagorean Theorem and Right Triangle Trig to solve for R and q…

adding vectors a strategy
Adding Vectors…A strategy

- Draw the vectors

  • Solve for the components of the vectors
  • Add the x components together
  • Add the y components together
    • NEVER ADD AN X COMPONENT TO A Y COMPONENT!
  • Redraw your new vector
  • Solve for the magnitude of the resultant vector (using Pythagorean Theorem)
  • Solve for the angle of the resultant vector (using tan)
some examples using the strategy
Some Examples Using the Strategy
  • A hunter walks west 2.5km and then walks south 1.8km. Find the hunter’s resultant displacement (distance and direction).
  • A man lost ina maze makes three consecutive dispacements so that at the end of the walk he is right back where he started. The first displacement is 8.00m westward, and the second is 13.0m northward. Find the magnitude and direction of the third displacement.
  • A rock is thrown with a velocity of 23.5m/s at an angle of 22.5 degrees to the horizontal. Find the horizontal and the vertical velocity components.
  • A boat is rowed east across a river with a constant speed of 5.0m/s. If the current is 1.5m/s to the south, what direction must the boat row to get straight across? What is the speed that it makes good?