Welcome back to Physics 211 If you need to work on your laptop during the lecture, please sit at the back of the room so you don’t distract other students. Get to know the people next to you, and work with them on the clicker questions during class. You will enjoy yourself and learn more. The room is very full – please move toward the center and help others find a seat.

Your Comments Boat problems I had physics 100, so it is familiar to me. I would like to discuss more about the vector stuff. I thought it was great! actual battleships should be destroyed in class. The subtraction of vectors to produce an acceleration vector is something I have not seen in previous physics studies and caused me slight confusion. Please go over both of the three ships questions. Very informative. I have no gripes. It took me a little bit to understand how the vectors worked, but now I think I have the hang of it. Some further explanation would help. The destroyer problems and wording were difficult. How can you tell which ship will be hit first when the initial speed is the same, and when it is different? Are we expected to be able to do numerical vector calculations or just understand the basics (with arrows)? Also, a lot of equations were shown during the pre- lecture, most of which can be derived with the knowledge of basic concepts. Are we expected to explicitly memorize any of them?

Lets do a quick recap of calculus concepts from last lecture…

In other words, v(t 1 ) tells us how x(t) is changing at time t 1. “Differentiating” is just finding the “Slope”28 t x(t) evaluated at t 1 t1t1 Slope at t 1

“Integrating” is just finding the “Area”42 How does this tell you distance? This is easy to see if you start by considering the case of constant velocity v 0. t v(t) v0v0 titi tftf tv(t) v0v0 titi tftf = velocity x time In this case the integral is easy to evaluate:

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

 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

Vector Addition

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

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

Another way to think of subtraction 1) Put vectors tail to tail Vectors and are shown to the right. Which of the following best describes  2) – is the vector pointing from the head of to the head of

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

Kinematics in 3D Three directions are independent but share time

Horizontal Vertical Boring Projectile Motion

A) The launched marble hits first. B) The dropped marble hits first. C) They both hit at the same time. DEMO Checkpoint A physics demo launches one marble horizontally while at the same instant dropping a second marble straight down. Which one hits the ground first? The initial vertical velocity on both is 0, and they are both only affected by the same force, gravity. They accelerate at the same rate and so hit and the same time.

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 v train car

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

Monkey x  x o Dart x  v o t 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 x = v ox t

v train car

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

The Ship Problems Mechanics Lecture 2, Slide 23 “I always have trouble solving purely conceptual problems/problems without numbers.”

Enemy 1DestroyerEnemy 2 A) Enemy 1 B) Enemy 2 C) They are both hit at the same time 60% of you got this one right…lets try again Checkpoint 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.

Checkpoint …Which enemy ship gets hit first? A) Enemy 1 B) Enemy 2 C) Same B) The height for 2 is lower than 1 C) Both shells were fired with the same initial velocity A) Enemy 1 is closer Enemy 1DestroyerEnemy 2Enemy 1Enemy 2

Enemy 1Destroyer Checkpoint 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

Enemy 1DestroyerEnemy 2 B) It has a greater horizontal component meaning it will be hit first. C) Since both shells reach the same height, their time in the air must be the same as well. A) The distance traveled to ship one is less. …Which enemy ship gets hit first? A) Enemy 1 B) Enemy 2 C) Same Checkpoint

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