gps - dr. wagner, chamblee charter high school · properties of vectors •vectors can be moved...
TRANSCRIPT
![Page 1: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/1.jpg)
![Page 2: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/2.jpg)
GPS
• SP1. Students will analyze the relationships
between force, mass, gravity, and the motion of
objects.
– b. Compare and contrast scalar and vector quantities.
![Page 3: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/3.jpg)
SCALARS AND VECTORS
• Scalars only have magnitude (ex. 50 m)
• Vectors have magnitude and direction (ex. 50
m, North)
• When you combine two or more vectors the
sum is called the resultant.
• For example in 1-D:
50 m North and 30 m South;
the resultant is 20 m North (+50 m + (-30 m))
![Page 4: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/4.jpg)
VECTOR BASICS
Images:
http://www.physicsclassroom.com/Class/vec
tors/u3l1a.cfm
![Page 5: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/5.jpg)
THE RESULTANT IN ONE
DIMENSION
htt
p:/
/ww
w.p
hy
sicsc
lass
roo
m.c
om
/Cla
ss/v
ecto
rs/
U3
l1b
.cfm
![Page 6: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/6.jpg)
DIRECTION
Images:
http://www.physicsclassroom.com/Class/vectors/u
3l1a.cfm
![Page 7: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/7.jpg)
htt
p:/
/ww
w.p
hysi
cscl
ass
room
.com
/mm
edia
/vec
tors
/vd
.cfm
![Page 8: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/8.jpg)
THE RESULTANT IN TWO
DIMENSIONS (X AND Y)
http://www.physicsclassroom.com/Class/vect
ors/U3l1b.cfm
![Page 9: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/9.jpg)
![Page 10: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/10.jpg)
PROPERTIES OF VECTORS• Vectors can be moved parallel to themselves in
a diagram.
• Vectors can be added in any order. For
example, A + B is the same as B + A
• To subtract a vector, add its opposite. SIGNS
(DIRECTION) ARE VERY IMPORTANT!!!
• Multiplying or dividing vectors by scalars
results in vectors. For example: When you
divide displacement (x or y) by time (s) the
result is velocity (v).
![Page 11: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/11.jpg)
http://www.physicsclassroom.com/mmedia/vectors/ao.cfm
![Page 12: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/12.jpg)
RESULTANTS CAN BE DETERMINE
GRAPHICALLY OR
ALGEBRACIALLY
• When determining the resultant graphically you must be
careful of several factors.
• Your scale must be determined and measured
accurately with a ruler.
• Your angles (directions) must be done with a protractor.
• ALWAYS DRAW YOUR VECTORS FROM HEAD TO
TAIL!!!!!
• The resultant is always from the head of your last vector
to the tail of your first vector.
HEADTAIL HEAD
TAIL
![Page 13: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/13.jpg)
DETERMINING SCALE
http://www.physicsclassroom.com/Class/vectors/u3l1a.cfm
![Page 14: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/14.jpg)
GRAPHICALLY DETERMINING
A RESULTANThttp://www.physicsclassroom.com/Class/vectors/U3l1b.cfm
![Page 15: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/15.jpg)
Name that Vector!
• http://www.physicsclassroom.com/Physics-
Interactives/Vectors-and-Projectiles/Name-
That-Vector/Name-That-Vector-Interactive
![Page 16: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/16.jpg)
DETERMINING
RESULTANTS BY ALGEBRA
AND TRIGONOMETRY• You must use the Pythagorean theorem and
trigonometry to determine a resultant.
• WE ONLY USE DEGREES IN THIS CLASS!! NO
RADIANS!!!!
• You must know SOHCAHTOA!!
• You must be able to use your calculator correctly!
• The resultant is always from the head of your last vector
to the tail of your first vector.
• Direction is always from the tail of the first vector.
![Page 17: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/17.jpg)
![Page 18: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/18.jpg)
![Page 19: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/19.jpg)
![Page 20: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/20.jpg)
![Page 21: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/21.jpg)
![Page 22: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/22.jpg)
![Page 23: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/23.jpg)
Physics, September 28
•Grab a whiteboard
•Vector PRACTICE!!
![Page 24: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/24.jpg)
htt
p:/
/ww
w.p
hy
sics
cla
ssro
om
.co
m/C
lass
/vec
tors
/U3
l1b
.cfm
![Page 25: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/25.jpg)
htt
p:/
/ww
w.p
hy
sics
cla
ssro
om
.co
m/C
lass
/vec
tors
/U3
l1b
.cfm
![Page 26: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/26.jpg)
REAL LIFE VECTORSh
ttp
://w
ww
.ph
ysi
cscl
ass
roo
m.c
om
/mm
edia
/vec
tors
/pla
ne.
cfm
![Page 27: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/27.jpg)
htt
p:/
/ww
w.p
hy
sicsc
lass
roo
m.c
om
/Cla
ss/v
ecto
rs/
U3
l1b
.cfm
![Page 28: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/28.jpg)
ANSWERS TO PRACTICE
• PRACTICE A:
11.18 km at 26.56 º W of N OR
11.18 km at 63.44º N of W
• PRACTICE B:
50 km at 53.13º S of W OR
50 km at 36.87º W of S
![Page 29: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/29.jpg)
PROBLEMS 1 and 2• Which of the following quantities are scalars, and
which are vectors? (A) the acceleration of a
plane as it takes off (B) the number of passengers
on the plane (C) the duration of the flight (D) the
displacement of the flight (E) the amount of fuel
required for the flight?
• A roller coaster moves 85 m horizontally, then
travels 45 m at an angle of 30° above the
horizontal. What is its displacement from its
starting point?(graphical techniques)
![Page 30: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/30.jpg)
ANSWERS
30°
RESULTANT
126 m at 10° above the horizontal 126 m at
10° above the horizontal
•(A) vector (B) scalar (C) scalar (D) vector
•(E) scalar
![Page 31: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/31.jpg)
•TODAY: Turn in map
Worksheet (you have
until the end of class)
•Homework: Vector
worksheet, due
MONDAY
![Page 32: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/32.jpg)
PROBLEMS 3 and 4• A novice pilot sets a plane’s controls, thinking the
plane will fly at 250 km/hr to the north. If the
wind blows at 75 km/hr toward the southeast,
what is the plane’s resultant velocity? Use
graphical techniques.
• While flying over the Grand Canyon, the pilot
slows the plane’s engines down to one-half the
velocity of the last problem. If the wind’s
velocity is still 75 km/h toward the southeast,
what will the plane’s new resultant velocity be?
![Page 33: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/33.jpg)
ANSWERS
• 204 km/h at 75° north of east
• 89 km/h at 54° north of east
![Page 34: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/34.jpg)
PROBLEM
• The water used in many fountains is
recycled. For instance, a single water
particle in a fountain travels through an
85 m system and then returns to the same
point. What is the displacement of a
water particle during one cycle?
![Page 35: GPS - DR. WAGNER, CHAMBLEE CHARTER HIGH SCHOOL · PROPERTIES OF VECTORS •Vectors can be moved parallel to themselves in a diagram. •Vectors can be added in any order. For example,](https://reader034.vdocument.in/reader034/viewer/2022042123/5e9ee50c5084073f7d223d9f/html5/thumbnails/35.jpg)
ANSWER
• ZERO