CHAPTER 3 MOTION IN A PLANE Position vectors

CHAPTER 3 MOTION IN A PLANE

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

Velocity In A Plane vav = (r 2 -r 1) / (t 2–t 1) = Δr / Δt Components of the average velocity vectors are: vav, x= Δx / Δt and vav, y= Δy / Δt

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

Independence Of Horizontal And Vertical Motions

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. 1. 2. 3. 4. 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/s 2. The Earth’s rotation is ignored. The Earth’s curvature is ignored.

Constant-Acceleration Equations of Motion in Two. Dimensions vx = v 0 x + axt vy = v 0 y + ayt x = x 0 + v 0 xt + (½ )axt 2 y = y 0 + v 0 yt + (½ )ayt 2 vx 2 = v 0 x 2 + 2 ax(x – x 0) vy 2 = v 0 y 2 + 2 ay(y – y 0)

Determination of key items for projectiles • • • x = (vocos o)t = tan-1(vy/vx) y = (vosin o)t - ½gt 2 vx = vocos o vy = vosin o- gt

• UNIFORM CIRCULAR MOTION

Uniform Circular Motion

Centripetal Acceleration arad = v 2/R

• HOMEWORK: • 12, 17, 22, 36,

• 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?