Kinematic Curves Worksheet
•  Split the problems between the groups
•  Draw the position, velocity, and acceleration vs. time
graphs on whiteboards
•  Check your answers with other groups
•  Whiteboard:
•  Table 1 and Table 2 GP1
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page 1: 4, 5
•  Table 1 and Table 2 GP 2
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page 1: 7, 10
•  Table 3 and Table 4 GP 1
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page 2: 3, 4
•  Table 3 and Table 4 GP 2
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page 2: 6, 8
Ch. 3 Vectors
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Vectors and Scalars
Unit Vectors
Column Vectors
Magnitude, Direction
Cartesian and Polar Coordinates
Calculations: components, resultants
•  Trigonometry!
•  Lots of practice problems
Vectors and Scalars
•  scalar quantity
–  completely specified by a single value with an
appropriate unit and has no direction.
–  Use an italic letter: A
•  vector quantity
–  completely described by a number and
appropriate units plus a direction.
–  Use an arrow: A
General Physics
C1
3
Important Concepts
Column Vector
•  How can we describe position using a using
column vector?
typical vector notation
column vector notation
General Physics
C1
5
Using Vectors
Magnitude and Direction
•  A vector may also be represented by its magnitude
and direction.
•  Magnitude
•  The magnitude of the vector has physical units
•  The magnitude of a vector is always a positive
number
General Physics
C1
7
Direction
•  Based on forming
a right triangle
from r and θ
H
•  x = r cos θ
•  y = r sin θ
O
•  SOH-CAH-TOA
A
General Physics
C1
8
Cartesian to Polar Coordinates
•  r is the hypotenuse and θ
an angle
•  θ must be counterclockwise from positive x
axis for these equations
to be valid
General Physics
C1
9
Example problem
•  Jane leaves her house and
walks 5.0 blocks east and
then proceeds north until
she is 7.8 blocks from
home at an angle of 50
degrees North of east.
How many blocks north
did she travel?
General Physics
C1
10
Using Vectors
Using Vectors
Problems from the Student Workbook
•  p. 3-1: 1, 2, 5, 6
•  p. 3-2: 8, 10, 11, 13, 14
•  p. 3-3: all problems
•  p. 3-4: 26, 27, 28
•  Whiteboard your results
•  Use column vectors whenever possible
Practice - Problem 3.37
Mary needs to row her boat across a 120 m wide river that
is flowing to the east at a speed of 1.0 m/s . Mary can row
the boat with a speed of 2.0 m/s relative to the water.
a) If Mary rows straight north, how far downstream will
she land?
b) Draw a picture showing Mary s displacement due to
rowing, her displacement due to the river s motion, and
her net displacement.
•  Whiteboard!!!
Practice - Problem 3.41
A flock of ducks is trying to migrate south for the winter,
but they keep being blown off course by a wind blowing
from the west at 6.0 . A wise elder duck finally realizes
that the solution is to fly at an angle to the wind.
If the ducks can fly at 9.0 relative to the air, what direction
should they head in order to move directly south?
•  Whiteboard!!!