Warm Up

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Warm Up

• Draw a vector that goes towards the Northwest
• Draw and label the components of the vector
• Label the parts of the right triangle that you
  just created (opp, adj., hyp.)

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Magnitude

• The amount or size of something
• 10 pounds
• 10 meters
• 10 miles per hour

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Vector

• Vectors represent a magnitude and direction
• 10 mph, East
• 10 m/s, up
• 10 N, 30 up from horizontal

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Vector

• Graphically, look like this

Magnitude
Start, Head
End, Tail
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Scalar

• Represents just something with magnitude with no
  direction
• Graphically, look like this

Magnitude
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Vector Components

• Forms a right triangle with the vector
• Vector components go in the same direction as the
  original vector

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Vector Components

• Forms a right triangle with the vector
• Horizontal or x-component
• Vertical or y-component
• Vector components go in the same direction as the
  original vector

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Vector Addition

• Similar to vector components in reverse
• There are 2 methods
• Head to Tail
• Head to Head (aka parallelogram method)

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Vector Addition

• Resultant the final vector after adding all of
  the other vectors

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Vector Components

• The components of vectors are also vectors
• Vectors require a direction, so components also
  need to have an arrow

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Warm Up

• Find the missing sides and use proper units

H
35
55 km
X
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Keys to successful word problems

1. Read the problem carefully.
2. What is the question asking?
3. What information does it give us?
4. Draw the problem out.

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Vector Addition

• Head to Tail method
• Similar to connect the dots
• Where the first vector ends, the second begins
• Resultant is drawn from where you started towards
  where you ended

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Vector Addition

• Head to Head method
• Create a parallelogram by copying one vector to
  the other side
• Resultant is drawn from where both heads are
  towards where both tails are

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• An object moves with a velocity of 5.0 m/s at an
  angle of 30 above the x-axis. What are the x-
  and y-components of the velocity?

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• A swimmer can swim at 1 m/s directly towards the
  shore. If the current pushes the swimmer at 3 m/s
  West, what is the swimmers resultant vector?

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• A human cannonball is shot out with a horizontal
  component of 12 m/s and a vertical component of 5
  m/s. What is the angle with respect to the
  horizontal and speed of the daredevil?

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• The Space Shuttle is moving horizontally at 100
  m/s. If it applies enough thrust to change its
  current heading by 15 up, what was the vector of
  the thrust and how fast is the shuttle moving
  afterwards?

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Warm Up

• An airplane flies into a headwind of 50 m/s. What
  is the airplanes speed if it normally flies 300
  m/s?

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SOH CAH TOA

• Calculate the value of ?

15 m/s
75
?
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SOH CAH TOA

• Calculate the value of ?

125 m/s2
33
?
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SOH CAH TOA

• Calculate the value of ?

?
55
80 N
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SOH CAH TOA

• Calculate the value of ?

70 km
?
55 km
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SOH CAH TOA

• Calculate the value of ?

65 m/s
33
?
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SOH CAH TOA

• Calculate the value of ?

30 N
8 N
?
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• A car is driving West at 25 m/s into a head wind.
  How strong is the head wind if the cars original
  speed is 30 m/s?

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• A runner goes 50.0 m East, then 50.0 m South,
  then 50.0 m North, then 100 m West. What is the
  final displacement of the runner?

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• A slingshot shoots a pebble into the sky with a
  constant velocity of 10 m/s at an angle of 50
  above the ground. What is the vertical component
  of the pebbles vector?

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• A flying squirrel jumps and glides from one tree
  to another in an easterly direction. If the
  squirrel started at 50.0 m above the ground and
  landed at 20.0 m above ground, what is the angle
  of its descent with respect to the ground if the
  two trees are 100. m apart?

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Warm Up

• A model rocket is launched straight up into the
  sky. There is a very strong wind blowing from the
  East at 50 miles per hour. If the rocket flies at
  an angle of 50 degrees from vertical, what is the
  magnitude of the rockets vector?