Lecture 02: 2D Kinematics

Physics 2210Fall Semester 2014

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!

“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) Vectorsb) Projectile motion

Mechanics Lecture 2, Slide 4

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

Mechanics Lecture 2, Slide 5

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

Vectors

A

A

Mechanics Lecture 2, Slide 6

Vector Addition

Mechanics Lecture 2, Slide 7

A B C D

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

Flashcard Question

A

B

Mechanics Lecture 2, Slide 8

A B C D

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

Flashcard Question

A

B

Mechanics Lecture 2, Slide 9

A B C D

Vectors A and B are shown to the right. Which of the following best describes A - B?

Flashcard Question

A

B

Mechanics Lecture 2, Slide 10

A B C D

Vectors A and B are shown to the right. Which of the following best describes A - B?

Flashcard Question

A

B

Mechanics Lecture 2, Slide 11

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

Vectors in 3D

Mechanics Lecture 2, Slide 12

Kinematics in 3D

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 inthe absence of air resistance, all

objects fall with the same constantacceleration (g = 9.81 m/s2).

- Galileo

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!

Mechanics Lecture 2, Slide 15

Horizontal Vertical BoringBoring

Projectile Motion

Mechanics Lecture 2, Slide 16

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

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?

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?

Mechanics Lecture 2, Slide 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 monkeyB) Below the monkeyC) Above the monkey

Mechanics Lecture 2, Slide 19

Monkey

x = xo

Dart

x = vo t

2

2

1gty −=

Shooting the Monkey…

2

2

1gty −=

Mechanics Lecture 2, Slide 20

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

Mechanics Lecture 2, Slide 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 monkeyB) Below the monkeyC) Above the monkey

Mechanics Lecture 2, Slide 22

Enemy 1Destroyer Enemy 2

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

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?

Number 1 “Lecture Thoughts” Question!

Mechanics Lecture 2, Slide 23

Enemy 1Destroyer Enemy 2

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

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?

Number 1 “Lecture Thoughts” Question!

Mechanics Lecture 2, Slide 24

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

Mechanics Lecture 2, Slide 25

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

Mechanics Lecture 2, Slide 26

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?

D

3 m

y

x

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?