1. S-11 A squirrel shoots his machine gun at the evil
bunny family across the street. If the bullet
starts from rest and exits the barrel at 1000
m/s, what is the acceleration of the bullet.
Assume that the barrel
is .35 m long.

2. Vec t o r s
Unit 2

3. 2.1 Scalars Versus Vectors

4. b. Compare and contrast scalar and vector quantities.
SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects.
b. Compare and contrast scalar and vector quantities.
Standard

5. Scalar – number with units (magnitude)
Vector – has both magnitude and direction
displacement
velocity
acceleration
Vector notation – letter with arrow
2.1 Scalars Versus Vectors
Compare and contrast scalar and vector quantities.

6. 2.2 The Components of a Vector
Compare and contrast scalar and vector quantities.

7. Vectors can be broken down into components
A fancy way of saying how far it goes on the x and on the y
2.2 The Components of a Vector
Compare and contrast scalar and vector quantities.

8. We calculate the sides using trig
2.2 The Components of a Vector
Compare and contrast scalar and vector quantities.

9. A represents any vector
2.2 The Components of a Vector
Compare and contrast scalar and vector quantities.

10. Then we can calculate the y
2.2 The Components of a Vector
Compare and contrast scalar and vector quantities.

11. For example if a vector that is 45 m @ 25o
2.2 The Components of a Vector
Compare and contrast scalar and vector quantities.

12. Practice Components of Vectors
Compare and contrast scalar and vector quantities.

13. Magnitude is calculated using the Pythagorean theorem
If we know the components you can calculate the original the value of the vector.
Magnitude is calculated using the Pythagorean theorem
2.2 The Components of a Vector
Compare and contrast scalar and vector quantities.

14. The direction is given as an angle from the +x axis
Positive is counterclockwise
2.2 The Components of a Vector
Compare and contrast scalar and vector quantities.

15. Practice Resolving Vectors
Compare and contrast scalar and vector quantities.

16. 2.3 Adding and Subtracting Vectors
Compare and contrast scalar and vector quantities.

17. Steps in vector addition Sketch the vector a. Head to tail method
Always make a sketch of vector addition so you can approximate the correct answer
Vector Addition Applet
Steps in vector addition
Sketch the vector
a. Head to tail method
b. Parallelogram method
2.3 Adding and Subtracting Vectors
Compare and contrast scalar and vector quantities.

18. Compare and contrast scalar and vector quantities.
Break vectors into their components
Add the components to calculate the components of the resultant vector
Calculate the magnitude of R
Calculate the direction of R
a. Add 180o to q if Rx is negative
2.3 Adding and Subtracting Vectors
Compare and contrast scalar and vector quantities.

19. 2.3 Adding and Subtracting Vectors
Compare and contrast scalar and vector quantities.

20. Compare and contrast scalar and vector quantities.
When vectors are subtracted
The vector being subtracted has its direction changed by 180o
Then we follow the steps of vector addition
2.3 Adding and Subtracting Vectors
Compare and contrast scalar and vector quantities.

21. Compare and contrast scalar and vector quantities.
Practice Adding and Subtracting Vectors
Compare and contrast scalar and vector quantities.

22. S-12 A moose is trying out his new advanced
attack shuttle to hunt down defenseless
baby deer. He travels north for 100 m, then
goes o, and finally turns and
goes 211 m
@ -309o.
What is his
displacement?

23. 2.4 Motion in Two Dimensions

24. SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects.
f. Measure and calculate two-dimensional motion (projectile and circular) by using component vectors.
Standard

25. 2.4 Motion in Two Dimensions
Projectile Motion – object traveling through space under the influence of only gravity
From the moment it is launched until the instant before it hits the ground
2.4 Motion in Two Dimensions
Measure and calculate two-dimensional motion by using component vectors.

26. 2.4 Motion in Two Dimensions
Acceleration is caused by gravity
In what axis?
Only in the y
What happens in the x?
Constant velocity
2.4 Motion in Two Dimensions
Measure and calculate two-dimensional motion by using component vectors.

27. 2.4 Motion in Two Dimensions
So if there is no gravity
2.4 Motion in Two Dimensions
Measure and calculate two-dimensional motion by using component vectors.

28. 2.4 Motion in Two Dimensions
In the y axis, acceleration is always -9.80m/s2
All the acceleration equations apply
In the y axis motion is identical to falling
2.4 Motion in Two Dimensions
Measure and calculate two-dimensional motion by using component vectors.

29. 2.4 Motion in Two Dimensions
The actual pathway has constant x velocity and changing y
Acceleration in the -y
Projectile
2.4 Motion in Two Dimensions
Measure and calculate two-dimensional motion by using component vectors.

30. 2.5 Projectile Motion: Basic Equations
Measure and calculate two-dimensional motion by using component vectors.

31. 2.5 Projectile Motion: Basic Equations
We will assume
no air resistance
gravity is 9.80 m/s2
the Earth is not moving (Frame of Reference)
That leaves the following variables X Y
vx =
voy =
x =
vy =
t =
a = m/s2
y =
2.5 Projectile Motion: Basic Equations
Measure and calculate two-dimensional motion by using component vectors.

32. 2.5 Projectile Motion: Basic Equations
The two axis are independent of each other except for time X Y
vx =
voy =
x =
vy =
t =
a = m/s2
y =
2.5 Projectile Motion: Basic Equations
Measure and calculate two-dimensional motion by using component vectors.

33. 2.6 Zero Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

34. If an object is launched at 0o vx = vcosq = vcosq = v
vy = vsinq = vsinq = 0
So our chart becomes X Y
vx = v
voy = 0
x =
vy =
t =
a = m/s2
y =
2.6 Zero Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

35. Now we can fill in whatever else is given in the problemX Y
vx = v
voy = 0
x =
vy =
t =
a = m/s2
y =
2.6 Zero Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

36. A person on a skate board with a constant speed of 1
A person on a skate board with a constant speed of 1.3 m/s releases a ball from a height of 1.25 m above the ground.
What variable can you
fill in? X Y
vx = v
voy = 0
x =
vy =
t =
a = m/s2
y =
2.6 Zero Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

37. A person on a skate board with a constant speed of 1
A person on a skate board with a constant speed of 1.3 m/s releases a ball from a height of 1.25 m above the ground.
What variable can you
fill in? X Y
vx = 1.3m/s
voy = 0
x =
vy =
t =
a = m/s2
y = m
2.6 Zero Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

38. We are now prepared to answer some questions
A) How long is the ball in the air? X Y
vx = 1.3m/s
voy = 0
x =
vy =
t =
a = m/s2
y = m
2.6 Zero Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

39. We are no prepared to answer some questions
A) How long is the ball in the air? X Y
vx = 1.3m/s
voy = 0
x =
vy =
t = 0.505s
a = m/s2
y = m
2.6 Zero Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

40. Basically a one dimensional problem
Notice that time is the same in both the Y and the X X Y
vx = 1.3m/s
voy = 0
x =
vy =
t = 0.505s
a = m/s2
y = m
2.6 Zero Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

41. We can now solve for X variable if we want
B) What is the x displacement? X Y
vx = 1.3m/s
voy = 0
x =
vy =
t = 0.505s
a = m/s2
y = m
2.6 Zero Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

42. We can now solve for X variable if we want
B) What is the x displacement? X Y
vx = 1.3m/s
voy = 0
x =0.656m
vy =
t = 0.505s
a = m/s2
y = m
2.6 Zero Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

43. Practice Zero Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

44. S-13
A pig is tied to a rocket and shot upward with an acceleration of 5 m/s2 at an angle of 35o. After 4 seconds, what is the x and y component of his velocity?

45. 2.7 General Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

46. All that changes if the launch angle is not zero vx = vcosq vy = vsinq
voy =
x =
vy =
t =
a = m/s2
y =
2.7 General Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

47. Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35o. What is displacement after 1.00s? X Y
vx =
voy =
x =
vy =
t = 1.00s
a = m/s2
y =
2.7 General Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

48. Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35o. What is displacement after 1.00s?
vx = vcosq =20cos35
vx = 16.4m/s X Y
vx =
voy =
x =
vy =
t = 1.00s
a = m/s2
y =
2.7 General Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

49. Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35o. What is displacement after 1.00s?
vx = vcosq =20cos35
vx = 16.4m/s X Y
vx = 16.4m/s
voy =
x =
vy =
t = 1.00s
a = m/s2
y =
2.7 General Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

50. Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35o. What is displacement after 1.00s?
vy = vsinq = 20sin35
vx = 11.5 m/s X Y
vx = 16.4m/s
voy =
x =
vy =
t = 1.00s
a = m/s2
y =
2.7 General Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

51. Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35o. What is displacement after 1.00s?
vy = vsinq = 20sin35
vx = 11.5 m/s X Y
vx = 16.4m/s
voy = 11.5m/s
x =
vy =
t = 1.00s
a = m/s2
y =
2.7 General Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

52. Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35o. What is displacement after 1.00s?
x = vt
x = (16.4)(1) = 16.4 X Y
vx = 16.4m/s
voy = 11.5m/s
x =
vy =
t = 1.00s
a = m/s2
y =
2.7 General Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

53. Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35o. What is displacement after 1.00s?
x = vt
x = (16.4)(1) = 16.4 X Y
vx = 16.4m/s
voy = 11.5m/s
x = 16.4 m
vy =
t = 1.00s
a = m/s2
y =
2.7 General Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

54. Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35o. What is displacement after 1.00s?
y=voyt+½at2
y=11.5(1)+½(-9.8)(1)2
y=6.6m X Y
vx = 16.4m/s
voy = 11.5m/s
x = 16.4 m
vy =
t = 1.00s
a = m/s2
y =
2.7 General Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

55. displacement (magnitude)
Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35o. What is displacement after 1.00s?
displacement (magnitude) X Y
vx = 16.4m/s
voy = 11.5m/s
x = 16.4 m
vy =
t = 1.00s
a = m/s2
y = 6.6m
2.7 General Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

56. displacement (magnitude) = 17.7 m direction
Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35o. What is displacement after 1.00s?
displacement (magnitude) = 17.7 m
direction X Y
vx = 16.4m/s
voy = 11.5m/s
x = 16.4 m
vy =
t = 1.00s
a = m/s2
y = 6.6m
2.7 General Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

57. Practice General Launch Angle
Measure and calculate two-dimensional motion by using component vectors.

58. S-14 The Blue Aardvark throws an ant off a tall hill. If the
ant is thrown 55 22o,
what is the maximum height
that he reaches?

59. Practice
Measure and calculate two-dimensional motion by using component vectors.

60. A-15 A gopher is out worshipping the sun god,
when a bird swoops down and grabs him.
The bird is climbing with a velocity of 55 m/s @ 62o when he drops the gopher. If the gopher was above the ground at the time, with what velocity does he strike the soft heather?

61. Practice
Measure and calculate two-dimensional motion by using component vectors.

62. A-16 A dancing 2000 kg hippo leaps gracefully
into the air. If she reaches a maximum
height of 0.45 m
and leaps at an
angle of 35o. What
was her initial velocity?
What is her hang -
time?

63. Practice
Measure and calculate two-dimensional motion by using component vectors.

64. S-17 A killer tomato leaps at an unsuspecting dancing lady. If the
tomato jumps with an initial velocity of 200
64o and lands on
her 0.45 m above the
ground, how far was he
when he jumped?

65. Practice
Measure and calculate two-dimensional motion by using component vectors.

66. S-18 A really cute bunny is tossed by his friends over
a fence to a garden. If his initial velocity is
15 30o, and he starts from 5 m before the 2 m tall
fence. Does he clear
the fence? How much
above or below the top
of the fence does he go
over (or hit)?

67. Practice
Measure and calculate two-dimensional motion by using component vectors.

68. S-19 Dude is out jumping his windsurfer dude,
when he catches a really cool wave dude. If
the dude gets way up and like dude he
reaches a height of
11.2 m. If he, dude,
took off at an angle
of 51o, dude..what
was his original
Velocity? Dude!

69. Practice
Measure and calculate two-dimensional motion by using component vectors.

70. S-20 Three Giraffes named Ira, Samuel, and
Lissette are singing a happy song when they
are pushed off the cliff by an angry Badger.
If they are pushed horizontally off a cliff that
is 2000 m tall, with a speed of 114 m/s, how
long do they have to
keep singing their
happy song. (any
resemblance to real
students is just a
random coincidence)

71. Practice
Measure and calculate two-dimensional motion by using component vectors.

72. S-21 A wolf named Sam is doing his best victory dance
because his mom gave him
a tasty package of dried
squid. When an angry taco
eating giraffe pushed him
off a cliff. If the initial velocity of the wolf is 175
72o, what is the maximum height
that the wolf reaches. (still no resemblance
to any students)

73. Practice
Measure and calculate two-dimensional motion by using component vectors.

74. S-22 Kermit “Baby Face” Frog shoots his AK-47 at an
angle of 37o. The muzzle
velocity of the gun is 700
m/s in the general direction of Miss
Piggy. If the bullet lands at her
feet, and Kermie shot the gun
from 0.40 m in the air, how far
away was Miss Piggy?

75. Practice
Measure and calculate two-dimensional motion by using component vectors.

76. People Dying Everywhere
S-23
A little song for your
testing enjoyment
Oh Happy Test Day
Sorrow and Despair
People Dying Everywhere