Transcript Vectors_Intro.ppt

The Lunchroom Walk Revisited
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Remember the difference between
“scalar” and “vector” quantities?
When we describe motion using
diagrams, we are referring to vectors.
Let’s draw a vector diagram of our trip
to the lunch room…
120 m
50 m
80 m
Physics
Room
Cafeteria
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The total distance traveled was 250 m
Our trip could have been shortened if
we could have gone in a straight line
(“as the crow flies”)
This straight line distance is called
displacement
120 m
50 m
Cafeteria
80 m
Displacement
Physics
Room
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The vectors that make the distance can be
combined to find displacement
To combine vectors:
◦ Vectors that travel in the same direction are added
◦ Vectors that travel in opposite directions are
subtracted
◦ Vectors at angles can be combined using trig
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120 m
50 m
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Cafeteria
80
m
Displacement
Physics
Room
The displacement to
the right is 120 m
The displacement up
is a combination of
two vectors:
◦ 80 m up
◦ 50 m down
◦ Net displacement = 30
m up
120 m
Cafeteria
30 m
Displacement
Physics
Room
How do we find total displacement?
•Pythagorean Theorem
•a2 + b2 = c2
•302 + 1202 = c2
•c = 124 m
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Not quite, since
displacement is a
magnitude and
direction…what
direction does our
displacement go?
We can use trig to
find the angle
Yipee!
120 m
Cafeteria
30 m
Displacement
How do we find the angle?
Physics
Room
•SOHCAHTOA
•Sine (a) = opp/hyp
•Sine (a) = 120/124
•(a) = sine-1 (120/124)
•(a) = 75°
Our overall displacement would be described
as:
124 m, 75° east of north
Or
124 m, 15° north of east
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Chapter 4
#19, 24, 27, 28,
30, 33, 34
Make sure to
show your work
and label all
answers to
receive full credit!