1. CHAPTER 3 MOTION IN A PLANE

2. Position vectors can specify the location and displacement of a point in an x-y coordinate system

3. Components of the average velocity vectors are: vav,x= Δx / Δt
Velocity In A Plane
vav = (r2-r1) / (t2–t1) = Δr / Δt
Components of the average velocity vectors are:
vav,x= Δx / Δt
and vav,y= Δy / Δt

4. At every point along the path, the instantaneous velocity vector is tangent to the path.

5. Independence Of Horizontal And Vertical Motions

7. PROJECTILE MOTION
A projectile is any object that is given an initial velocity and then follows a path determined entirely by the effects of gravitational acceleration and air resistance.
In studying projectile motion we make the following assumptions:
Air resistance is ignored.
The acceleration of gravity is constant, downward, and has a magnitude equal to g = 9.81 m/s2.
The Earth’s rotation is ignored.
The Earth’s curvature is ignored.

10. Constant-Acceleration Equations of Motion in Two-Dimensions
vx = v0x + axt
vy = v0y + ayt
x = x0 + v0xt + (½ )axt2
y = y0 + v0yt + (½ )ayt2
vx2 = v0x2 + 2ax(x – x0)
vy2 = v0y2 + 2ay(y – y0)

11. Determination of key items for projectiles
x = (vocos o)t
 = tan-1(vy/vx)
y = (vosin o)t - ½gt2
vx = vocoso
vy = vosino- gt

12. UNIFORM CIRCULAR MOTION

15. Uniform Circular Motion

16. Centripetal Acceleration
arad = v2/R

17. HOMEWORK:
12, 17,22,36,

18. A daring 510 N swimmer dives off a cliff with a running horizontal leap, as shown in the figure below.  
What must her minimum speed be just as she leaves the top of the cliff so that she will miss the ledge at the bottom, which is 1.75 m wide and 9.00 m below the top of the cliff?