Lecture 02: 2D Kinematics. Physics 2210 Fall Semester 2014

Transcription

1 Lecture 02: 2D Kinematics Physics 2210 Fall Semester 2014

2 Announcements Note that all Prelectures, Checkpoint Quizzes, and Homeworks are available one week before due date. You should have done Prelecture 2 and Checkpoint 2 by now. Unit 2 Homework due 5:00 PM tomorrow 38% have already attempted Good, but I'd like to see this number increased!

3 Lecture Thoughts Responses Vector, trigonometry review Its not intuitive that x and y components of motion are independent. How is maximum height determined? 3-ships checkpoint problem numerical examples Today's Concepts: a) Vectors b) Projectile motion

4 Vectors A A y A x 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 Mechanics Lecture 2, Slide 4

5 Vectors A A θ 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 Mechanics Lecture 2, Slide 5

6 Vector Addition Mechanics Lecture 2, Slide 6

7 Flashcard Question A Vectors A and B are shown to the right. Which of the following best describes A + B? B A B C D Mechanics Lecture 2, Slide 7

8 Flashcard Question A Vectors A and B are shown to the right. Which of the following best describes A + B? B A B C D Mechanics Lecture 2, Slide 8

9 Flashcard Question A Vectors A and B are shown to the right. Which of the following best describes A - B? B A B C D Mechanics Lecture 2, Slide 9

10 Flashcard Question A Vectors A and B are shown to the right. Which of the following best describes A - B? B A B C D Mechanics Lecture 2, Slide 10

11 Vectors in 3D A vector can be defined in 2 or 3 (or even more) dimensions: Mechanics Lecture 2, Slide 11

12 Kinematics in 3D Mechanics Lecture 2, Slide 12

13 Projectile Motion Motion of an object which, after being given an initial velocity, is acted upon only by the force of gravity. Neglect air resistance Force of Gravity?? At a given location on Earth, and in the absence of air resistance, all objects fall with the same constant acceleration (g = 9.81 m/s 2 ). - Galileo

14 Projectile Motion To simplify kinematics equations, choose x is direction of horizontal component of initial velocity y is vertical direction, i.e. the direction in which all acceleration occurs Then Motion in x constant velocity Motion in y constant acceleration No motion in z!

15 Projectile Motion Horizontal Vertical Boring Mechanics Lecture 2, Slide 15

16 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? A) The launched marble hits first. B) The dropped marble hits first. C) They both hit at the same time. Mechanics Lecture 2, Slide 16

17 Example: A ball rolls with speed 5.00 m/s off the edge of a table. The table is 1.00 meter high. How far does the ball move horizontally before hitting the floor?

18 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 Mechanics Lecture 2, Slide 18

19 Shooting the Monkey Dart x = v o t 1 y = gt 2 2 Monkey x = x o 1 y = gt 2 2 Mechanics Lecture 2, Slide 19

20 Shooting the Monkey Still works even if you shoot upwards! y = y o 1 / 2 g t 2 y = v oy t 1 / 2 g t 2 Dart hits the monkey Mechanics Lecture 2, Slide 20

21 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 Mechanics Lecture 2, Slide 21

22 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? Destroyer Enemy 1 Enemy 2 A) Enemy 1 B) Enemy 2 C) They are both hit at the same time Number 1 Lecture Thoughts Question! Mechanics Lecture 2, Slide 22

23 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? Destroyer Enemy 1 Enemy 2 A) Enemy 1 B) Enemy 2 C) They are both hit at the same time Number 1 Lecture Thoughts Question! Mechanics Lecture 2, Slide 23

24 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? Destroyer Enemy 1 Enemy 2 A) Enemy 1 B) Enemy 2 C) They are both hit at the same time Mechanics Lecture 2, Slide 24

25 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? Destroyer Enemy 1 Enemy 2 A) Enemy 1 B) Enemy 2 C) They are both hit at the same time Mechanics Lecture 2, Slide 25

26 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 x 3 m D Mechanics Lecture 2, Slide 26

27 Field goal follow-up: Kicker is 80 meters from the goal posts. The ball is kicked at 30 m/s at an angle of 25 w.r.t. the ground. Will the kick clear the goal posts?

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