Physics 211Lecture 2

Today's Concepts:a) Vectorsb) Projectile motionc) Reference frames

Think of a vector as an arrow. (An object having both magnitude and direction)

The object is the same no matter how we chose to describe it

Ax

Ay

Vectors

A

5

A A vectorvector AA may be shown is bold may be shown is boldface or with an arrow over it. Weface or with an arrow over it. Wewill usually use the “arrow notation”;will usually use the “arrow notation”;That is certainly easier in your hand-That is certainly easier in your hand-written notes!written notes!

Think of a vector as an arrow. (An object having both magnitude and direction)

The object is the same no matter how we chose to describe it

Ax

Ay

Vectors

A

5

Think of a vector as an arrow. (An object having both magnitude and direction)

The object is the same no matter how we chose to describe it

Vectors

A

5

Vector Addition

7

A B C D E

Vectors and are shown to the right. Which of the following best describes +

A

ACT

B

A

B

A

B

9

A B C D E

Vectors and are shown to the right. Which of the following best describes

A

ACT

B

A

B

A

B

11

B

2

A B C D E

Vectors and are shown to the right. Which of the following best describes +

A

ACT

B

AA

A

B

13

A vector can be defined in 2 or 3 (or even more) dimensions:

Vectors in 3D

14

A vector can be defined in 2 or 3 (or even more) dimensions:

Vectors in 3D

14

A vector can be defined in 2 or 3 (or even more) dimensions:

Vectors in 3D

14

Scalar quantities, like the Scalar quantities, like the magnitudemagnitude of a vector, show up of a vector, show up notnot in bold and in bold and withwithoutout an arrow. To an arrow. To emphasizeemphasize this, this, we may use absolute value bars,we may use absolute value bars, A = | A = | AA | or A = | A | | or A = | A |

Kinematics in 3D

15

Three directions are independent but share time

Horizontal Vertical BoringBoring

Projectile Motion

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A) The launched marble hits first.B) The dropped marble hits first.C) They both hit at the same time.

DEMODEMO

Checkpoint 1

A physics demo launches one marble horizontally while at the same instant dropping a second marble straight down. Which one hits the ground first?

20

Both are accelerating downward with the same rate regardless of initial x velocity

A flatbed railroad car is moving along a track at constant velocity. A passenger at the center of the car throws a ball straight up. Neglecting air resistance, where will the ball land?

A) Forward of the center of the carB) At the center of the carC) Backward of the center of the car

correct

Demo - train

Ball and car start with same x position and x velocity, Since ax = 0 they always have same x position.

Train Demo ACT

vtrain car

23

Monkey Troubles

You are a vet trying to shoot a tranquilizer dart into a monkey hanging from a branch in a distant tree. You know that the monkey is very nervous, and will let go of the branch and start to fall as soon as your gun goes off. In order to hit the monkey with the dart, where should you point the gun before shooting?

A) Right at the monkeyB) Below the monkeyC) Above the monkey

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Monkey

x xo

Dart

x vo t

2

2

1gty

Shooting the Monkey…

2

2

1gty

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Shooting the Monkey…

y = voy t 1/2 g t 2

Still works even if you shoot upwards!y = yo 1/2 g t 2

Dart hits themonkey

30

vtrain car

Projectile Motion & Frames of Reference

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Time spent in air depends on vertical motion!

Enemy 1Destroyer Enemy 2

A) Enemy 1B) Enemy 2C) They are both hit at the same time

67% of you got this one right…lets try again

Checkpoint 2A destroyer simultaneously fires two shells with the same initial speed at

two different enemy ships. The shells follow the trajectories shown. Which ship gets hit first.

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Checkpoint 2…Which enemy ship gets hit first?A) Enemy 1 B) Enemy 2 C) Same

B) The shell fired at ship one goes higher in the vertical direction so it will be in the air longer since the vertical velocity determines the time of flight

C) Since they have the same initial speeds the two shells will hit both ships at the same time.

A) The vertical component is the same and therefore you can concentrate on the horizontal component. Enemy 1 is closer and will get hit first.

Enemy 1Destroyer Enemy 2Enemy 1 Enemy 2

Enemy 1Destroyer

Checkpoint 3A destroyer fires two shells with different initial speeds at two different

enemy ships. The shells follow the trajectories shown. Which enemy ship gets hit first?

Enemy 2

A) Enemy 1

B) Enemy 2

C) They are both hit at the same time

70% of you got this one right…lets try again

38

Enemy 1Destroyer Enemy 2

B) The initial speed of the shell fired at ship 2 is greater, so ship 2 gets hit first.

C) they both achieve the same height so they remain in the air the same amount of time

A) Since the initial speed for the first shell is lower, Enemy Ship 1 will be hit first.

…Which enemy ship gets hit first?A) Enemy 1 B) Enemy 2 C) Same

Checkpoint 3

5050

Field Goal ExampleA field goal kicker can kick the ball 30 m/s at an angle of 30 degrees w.r.t. the ground. If the crossbar of the goal post is 3m off the ground, from how far away can he kick a field goal?

y-direction

voy = vo sin(30o) = 15 m/s

y = yo + voyt + ½ at 2

3 m = 0 m + (15 m/s) t – ½ (9.8 m/s2) t 2

t = 2.8 s or t = 0.22 s.

x-direction

vox = vo cos(30o) = 26 m/s

D = xo + vox t + ½ at 2

= 0 m + (26 m/s)(2.8 s) + 0 m/s2 (2.8 s )2

= 72.8 m

D

3 m

y

x