Transcript Warm Up - Milan Area Schools

Warm Up
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1) Draw a vector
2) Vectors are defined by their
____________and ___________.
Finish Test
Vectors
• You CAN
– Move them
– Describe them by their magnitude and direction
• Magnitude means length or strength
– Break them into x and y components, and use
those to describe them
• Use Trig to find components
– Think of them as the hypotenuse of a right
triangle.
• One leg, parallel to x axis is x component
• One leg, parallel to y axis is y component
– Add (and Subtract) them
Vectors
• You CANNOT
– Turn them (change their direction)
– Make them longer or shorter
A Vector
Tip
Magnitude
Direction
Tail
Labeling Vectors
• Write the name of the vector with an arrow
over it.
– We can also write the name of the vector in
bold font
Adding Vectors
• When we add vectors we add them “Tail to
tip”
• For instance if A + B = C then we take
vectors A and B and we move one so that
its tail is touching the tip of the other. To
get the answer (Vector C) we draw a new
vector from the tail of the first vector to the
tip of the second vector
B
A
A+B
A+B=C
See? Tail to Tip
C
This is the
answer
Moodle
• Respond to the prompt in the forum for
this week.
• Read the prompt for next week. This is
homework. Due Nov. 14
Components
This vector is 4 units long.
X component = 4
Y component = 0
This vector is 3 units long.
X component = 0
Y component = 3
Components
Vector C
5
36.87°
The x component is the side along the x axis. This is
adjacent to the angle. We will use cos to find its length
Magnitude of Cx = Length of C,
Times the cosine of the angle or
This is Cx, the x
component of C.
Cx = C * cos 36.87
Cx =5 * cos 36.87
Cx = 4
Components
Vector C
5
36.87°
The y component is the side along the y axis. This is
adjacent to the angle. We will use sin to find its length
Cy
This is Cy, the y
component of
C.
Magnitude of Cy = Length of C,
Times the sine of the angle or
Cy = C * sin 36.87
Cy =5 * sin 36.87
Cx = 3
Components
• So vector C has
– X component = 4
– Y component = 3
– Overall (or net) magnitude of 5
• Notice that the components and
magnitude obey the Pythagorean theorem
Warm Up
Vector F has a magnitude of 10 and a
direction of 53.2 degrees above the x axis.
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A) Draw F.
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B) Find the x component of F.
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C) Find the y component of F
Notebook
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Page 1 - 3 -Table of contents
Page 4 - 7 - warm ups
Page 7 - 14 - Notes
Page 14 - 17 -Personal Physics Demons
Page 18 - 30 - Practice Problems
Page 31 - 50 - Homework
Adding vectors using components
• If we are adding two vectors, find the x
and y components of each one.
• Add the x components up (direction
matters!)
– What you get is the x component of the
resultant
• Add the y components up
– What you get is the y component of the
resultant
Adding vectors using components
• Use the components you found to make
the resultant Vector
Homework
• Pg 65 (Q 5-8; P 4, 5, 7-9a)
• P10