By the end of this unit, successful students will be able to:
1) Add, subtract, and resolve vectors in two dimensions, particularly displacement and velocity vectors so they can determine components of a vector along two specified, mutually perpendicular axes. (APBIA2a1)
2) Determine the net displacement of a particle and the change in velocity of a particle (APBIA2a2,3) (3-1à3-4)
3) Solve problems of Galilean relative motion in two dimensions including determining the location and/or velocity of a particle relative to another (APBIA2a2) (3-8)
4) Understand the motion of projectiles in a uniform gravitational field, so they can write down expressions for the horizontal and vertical components of velocity and position as functions of time, and sketch or identify graphs of these components
5) Use these expressions in analyzing the motion of a projectile that is projected with an arbitrary initial velocity
All assignments are due on the date listed. That is not the date they are assigned.
Due date Day Assignment
10/7 Wed Read: 3.1 – 3.4, 3.8
Ungraded: Do Questions: 5, 7, 14
Graded: Do Questions: 8, 16 (PS 7) (Goals 1,2,3)
10/8 Thu Ungraded: Do Problems: 9, 10, 36, 39, 41, 42, 47, 57
Graded: Do Problems: 37, 46 (PS 8) (Goals 1, 2, 3)
10/9 Fri Do for class discussion:
Ungraded: Problems: 9, 10, 36, 39, 41, 42, 47, 57
10/14 Wed Read: 3.5 – 3.7
Ungraded Do Questions: 15, 17, 19
Graded Do Questions: 18, 20 (PS 9) (Goals 4, 5)
10/21 Wed Ungraded: Do Problems: 17, 18, 24, 35, 63, 71, 72, 74
Graded: Do Problems: 30, 65 (PS 10) (Goals 4, 5)
10/22 Thu Test: Chapter 3: 2-D Kinematics, Relative motion, and Projectiles
- Prentice Hall's web page on Giancoli Chapter 3 Motion in 2-D
- Haliday, Resnick and Walker's page on Chapter 3 - Vectors (Calculus based)
- Haliday, Resnick and Walker's page on Chapter 4 - Motion in 2 and 3 Dimensions (Calculus based)
- In addition to his astronomical discoveries and his popularization of the telescope as an astronomical instrument, Galileo Galilei (1564-1642) is credited with uncovering the law of inertia as well as recognizing that near the surface of the Earth all bodies fall at the same rate of acceleration. In addition, he recognized that an object's velocity is dependent upon the frame of reference of the observer, and that the motion of an object could be described separately in vertical, and two horizontal dimensions, thus developing the concept of Galilean relativity. Rice University's Galileo Project details much of his history.
- Eric Ludlum maintains Siege Engine.com - a site centered around a Massachusetts group which designs and opperates catapults, trebuchets, and the like. Perfect for projectile motion, torque, potential energy and other mechanics problems.
- Right Triangle Trigonometry In this overview, I define elementary trigonometric functions as they relate to lengths of the sides of right triangles and the internal angles of those triangles. Sine, cosine, and tangent functions are defined as are their inverse functions.
- Vector Addition in Two Dimensions I first describe Vector addition conceptually and graphically and then mathematical methods involving trigonometry are introduced, including breaking vector addends into orthogonal components, adding the components, and using trigonometry and the Pythagorean theorem to determine the direction and magnitude of the resultant vector.
- Vector Addition: Example Problem 1 Having previously introduced a basic technique of vector addition with trigonometry, we work an example problem doing so. Three displacement vectors are added together. I illustrate graphically what it means to add them, and work a technique through for adding their x-components, then their y-components, building the x and y components of the resultant vector. From there the Pythagorean theorem is used to determine the magnitude of the resultant displacement, and inverse tangent is used to determine the direction of the resultant displacement.
- Galilean Relativity: Basics I describe Galilean Relativity, first through an example involving motion on a moving bus, in the frame of reference of the bus and in that of the road. Vector algebra equations are shown to illustrate key ideas for Galilean Relativity. The example shown is in one dimension.
- Galilean Relativity: Two-Dimensional Example Problem In this video we solve a relatively simple two-dimensional Galilean Relativity problem involving a boat crossing a moving river. Given the boat's velocity relative to the water, and the water's velocity relative to shore, the resultant velocity of the boat relative to the shore is determined.
- 2-D Kinematics and Ideal Projectile Motion In this video we sketch out the equations of motion for the general case of constant acceleration in two dimensions and then from there develop equations for the specific case of ideal projectile motions. We state the assumptions involved for ideal projectile motion including that all forces other than gravity are negligible, but also the conditions leading to g being considered constant in size and direction for the flight.
- Ideal Projectile Motion Example Problem: Zero initial vertical velocity For an example problem involving ideal projectile motion with no initial vertical speed, we determine, time of flight, horizontal range, and final velocity of the projectile - a person running off a diving board.
- Ideal Projectile Motion Example Problem 2: Same Launch and Landing Height In this ideal projectile motion problem we imagine a ball hit with some initial velocity at some angle above the horizontal and landing at the same height from which it was launched. We determine time of flight, horizontal range, and maximum height.
- Mechanical Universe 4: Inertia video includes projectile motion and relative motion. (Calculus based)
- Mechanical Universe 5: Vectors. Video from David Goodstein's series adapted from CalTech's freshman physics classes. (Calculus based)
- Frames of Reference Frames of reference, Galilean Relativity, Projectiles in constant v frames; Projectiles in constant a frames; accelerating frames and inertial frames; fictitious forces.