1. Friday(09/10): Introduction to Motion in Two Dimensions (Ch.3).

Determining range and maximum height of a projectile. HW: Read Ch.3,

pages 56-63 and solve prob. 3, 7, 13, & 15 on page 75.

2. Monday(09/13):  Addition of Relative Velocities, Planes in the Wind,

Interactions of ships and swimmers with stream velocity. HW: Read pages

63-67 and solve prob. 21, 27, & 31 on page 76.

3. Tuesday(09/14): Lab on Two Dimensional Motion. HW: Process Lab

Data and Read pages 67-74 and solve prob. 47, 49, & 51 on page 77.

4. Wednesday(09/15): Post-Lab Discussion. HW: Complete lab

report and write Abstract, due Friday.

5. Thursday(09/16): Review I for Ch.3. HW: Complete Review

Handout.

6. Friday(09/17): Review II for Ch.3. HW: Complete Review Handout.

7. Monday(09/20): TEST on Ch.3 - Motion in Two Dimensions.

HW: Go to web-site for notes on Ch.4 - Forces and Newton's The Laws

of Motion.

WEBSITE NOTES: AP Physics B, Ch.3 - Kinematics Two Dimensions.

SC.912.P.12.2: Analyze the motion of an object in terms of its position,

velocity, and acceleration (with respect to a frame of reference) as

functions of time.

In two-dimensional motion, the horizontal and vertical components of the

motion must be regarded independently. For these two directions we use

x and y, respectively. For example, if an object is projected from the

ground with a velocity v₀ at an angle of elevation θ₀, then we can use

SOHCAHTOA to find out how fast it is moving in the x and y directions.

1. An object launched from the ground at some angle θ₀ is called a projectile.

The path it travels is an inverted parabola called its trajectory. A classic

example would be the motion of golf ball when struck with a club. Can you

think of a few more?

2. The initial velocity in the x direction is v_0x = v₀·cos(θ₀). The velocity of

the object in the y direction is v_0y = v₀·sin(θ₀). The acceleration is that of

gravity which acts only in the y direction. It is given by a_y= -g = -9.8m/s².

The acceleration in the x direction is a_x = 0.

3. We still have the five motion formulas from the study of kinematics derived

by Galileo (1564-1642). We still know them as: (a) Δx = v_avg·Δt ,

(b) v_avg = (v₀+v)/2 , (c) v = v₀ + a·Δt , (d) v² = v₀² + 2a·Δx ,

(e) Δx = v₀ ·Δt + ½a·Δt² . The task now is to adjust these for the separate

x and y directions.

4. Doing this, we get the following set of kinematics equations to analyze

the motion of a projectile launched at an angle. (a) Δx = v₀·cos(θ₀)·Δt ,

(b) v_x= v₀·cos(θ₀), constant, (c) Δy = v₀·sin(θ₀)·Δt -½g·Δt², 

(d) v_y= v₀·sin(θ₀) - g·Δt , and (e) v_y² = v₀² ·sin(θ₀)² - 2g·Δy .

5. In the absence of air resistance a projectile has a constant horizontal

velocity and a constant downward free-fall acceleration which effects the

vertical velocity, subtracting 9.8m/s from it on the way up, and adding

9.8 m/s to it on the way down.

6. A frame of reference is a coordinate system for specifying the precise

location of objects in space. Maybe you have heard the expression, "It

depends on your frame of reference."

7. To two observers moving relative to each other there would not be

agreement on the displacements and velocities of an object in motion

when each is using his/her own frame of reference.

8. For example, a person standing in a moving subway car, and facing

towards the back of the car, drops a book. According to the frame of

reference of the person in the car, the book fell in a straight line to the

floor. An observer standing outside on the subway platform as the car

goes by, sees the book traveling in a parabolic path toward the floor.

9. Therefore, the motion of an object depends on your frame of reference.

This is also occurs when boats travel in moving streams and when planes

encounter moving air masses. Also, sometimes you hear about certain

records in track and field that are not allowed if it is determined that

athletes were "wind aided."

10. Make sure you use  these steps to solve any problem in Physics:

(i) read the problem and identify the given variables

(ii) determine what you are asked to solve for

(iii) find the correct formula to use

(iv) use Algebra or Trigonometry to isolate the unknown

(v) substitute-in the given information and simplify.