Physics 211 Lecture 2 Today's Concepts: a) Vectors b) Projectile motion c) 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 AxAx AyAy Vectors 5 A vector A may be shown is bold face or with an arrow over it. We will usually use the “arrow notation”; That is certainly easier in your hand- 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 AxAx AyAy Vectors 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 5

Vector Addition 7

A B C D E Vectors and are shown to the right. Which of the following best describes + ACT 9

A B C D E Vectors and are shown to the right. Which of the following best describes  ACT 11

A B C D E Vectors and are shown to the right. Which of the following best describes + ACT 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 magnitude of a vector, show up not in bold and without an arrow. To emphasize this, we may use absolute value bars, A = | A | or A = | A | A = | A | or A = | A |

Kinematics in 3D 15 Three directions are independent but share time

Horizontal Vertical Boring Projectile Motion 16

A) The launched marble hits first. B) The dropped marble hits first. C) They both hit at the same time. DEMO 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 car B) At the center of the car C) Backward of the center of the car correct Demo - train Ball and car start with same x position and x velocity, Since a x = 0 they always have same x position. Train Demo ACT v train 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 monkey B) Below the monkey C) Above the monkey 26

Monkey x  x o Dart x  v o t Shooting the Monkey… 27

Shooting the Monkey… y = v oy t  1 / 2 g t 2 Still works even if you shoot upwards! y = y o  1 / 2 g t 2 Dart hits the monkey 30

v train car

Projectile Motion & Frames of Reference 31 Time spent in air depends on vertical motion!

Enemy 1DestroyerEnemy 2 A) Enemy 1 B) Enemy 2 C) They are both hit at the same time 67% of you got this one right…lets try again Checkpoint 2 A 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. 34

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 1DestroyerEnemy 2Enemy 1Enemy 2

Enemy 1Destroyer Checkpoint 3 A 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 1DestroyerEnemy 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

50 Field Goal Example A field goal kicker can kick the ball 30 m/s at an angle of 30 degrees wrt the ground. If the crossbar of the goal post is 3m off the ground, from how far away can he kick a field goal? D 3 m y x More complicated problems with x and y such as the soccer problem, but with actual numbers

50 Field Goal Example A 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 v oy = v o sin(30 o ) = 15 m/s y = y o + v oy t + ½ at 2 3 m = 0 m + (15 m/s) t – ½ (9.8 m/s 2 ) t 2 t = 2.8 s or t = 0.22 s. x-direction v ox = v o cos(30 o ) = 26 m/s D = x o + v ox t + ½ at 2 = 0 m + (26 m/s)(2.8 s) + 0 m/s 2 (2.8 s ) 2 = 72.8 m D 3 m y x