INTRO TO VECTORS DeKalb County Schools by mikeholy

VIEWS: 144 PAGES: 26

• pg 1
```									                          GPS

• SP1. Students will analyze the relationships
between force, mass, gravity, and the motion of
objects.
– b. Compare and contrast scalar and vector quantities.
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))
VECTOR BASICS

Images:
http://www.physicsclassroom.com/Class/vec
tors/u3l1a.cfm
http://www.physicsclassroom.com/Class/vectors/U3l1b.cfm

DIMENSION
THE RESULTANT IN ONE
DIRECTION

Images:
http://www.physicsclassroom.com/Class/vectors/u
3l1a.cfm
http://www.physicsclassroom.com/mmedia/vectors/vd.cfm
THE RESULTANT IN TWO
DIMENSIONS (X AND Y)

http://www.physicsclassroom.com/Class/vect
ors/U3l1b.cfm
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).
http://www.physicsclassroom.com/mmedia/vectors/ao.cfm
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.
• The resultant is always from the head of your last vector
to the tail of your first vector.
DETERMINING SCALE

http://www.physicsclassroom.com/Class/vectors/u3l1a.cfm
GRAPHICALLY DETERMINING
A RESULTANT
http://www.physicsclassroom.com/Class/vectors/U3l1b.cfm
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
• 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.
http://www.physicsclassroom.com/Class/vectors/U3l1b.cfm
http://www.physicsclassroom.com/Class/vectors/U3l1b.cfm
http://www.physicsclassroom.com/mmedia/vectors/plane.cfm

REAL LIFE VECTORS
http://www.physicsclassroom.com/Class/vectors/U3l1b.cfm
• 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
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)
•(A) vector (B) scalar (C) scalar (D) vector
•(E) scalar
126 m at 10° above the horizontal 126 m at
10° above the horizontal
RESULTANT

30°
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?
• 204 km/h at 75° north of east
• 89 km/h at 54° north of east
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?