physics 121 3. kinematics in 2-d and vectors 3.1 vectors and scalars 3.2 addition of vectors -...
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Physics 121
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3. Kinematics in 2-D and Vectors
3.1 Vectors and Scalars
3.2 Addition of Vectors - Graphically
3.3 Subtraction and Scalar Multiplication
3.4 Addition of Vectors - Analytically
3.5 Projectile Motion
3.6 Projectile Motion Problems
3.7 Projectile Motion is Parabolic
3.8 Relative Velocity
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Example 3.1 . . . Can 3 + 4 = 5?
Give examples of Scalar and Vector quantities
You drive 3 miles East and then 4 miles North. How far are you from your starting point? 5 miles
What is the difference between distance and displacement?
Distance is a Scalar (has magnitude only) and displacement is a Vector (direction is also required).
Scalars: speed and densityVectors: velocity and force
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Trig Review
Pythagorean Theorem: a2 + b2 = c2
sin = opposite / hypotenuse = a /c
cos = adjacent / hypotenuse = b / c
tan = opposite / adjacent = a / b
c
b
a
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Example 3.2 . . . Vector Addition
You drive 3 miles East and then 4 miles Northeast. What is your net displacement (magnitude and direction)?Solve it (a) graphically (b) analytically
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Solution 3.2(a) . . . Graphical Vector Addition
3
4
450
?
?
E
N
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Solution 3.2(a) . . . Graphical Vector Addition
3
4
450
6. 4
260
E
N
Resultant displacement vector is 6.4 m, 260 North of East
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Solution 3.2(b) . . . Analytical Vector Addition
Vector X = V cos Y = V sin
3 at 00 3 0
4 at 450 2.8 2.8
Resultant 5.8 2.8
R2 = X2 + Y2
R2 = (5.8)2 + (2.8)2
R = 6.4
tan = Y / X
tan = 2.8 / 5.8
= 260
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A picture is worth 103 words !!!
3
4
2.83
2.8
5.8
2.86.4
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Projectile Motion
1. Which projectile reaches the ground first?
2. Which is moving faster just before impact?
Two objects are launched horizontally with different speeds
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Projectile Motion
1. Same Time
2. Different Speeds
Two objects are launched horizontally with different speeds
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Example 3.3 . . . Projectile Motion
Given h= 20 m and VH = 7 m/s. Calculate (a) Time to hit the ground (b) Range D (c) Impact Speed
h
D
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Solution 3.3 . . . Projectile Motion
V2 = (20)2 + (7)2
V = 21.2 m/s
h = ½ a t2
t = 2 s
D = (7 m/s)(2 s)
D = 14 m
Vv = 0 + atVv = 0 + (10)(2)Vv = 20 m/s
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Example 3.4 . . . Soccer Ball
A soccer ball is kicked and it is projected with a speed of 20 m/s at an angle of 300. How far away does it land?
D
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Solution 3.4 . . . Soccer Ball
D = (VH )(t) D = (20 cos 300)(2)D = 34.6 m
Vv = 20 sin 300 = 10 m/sSo air time is 1s (up) and 1s(down) = 2 s
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That’s all folks!