CHAPTER 3 MOTION IN A PLANE

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CHAPTER 3 MOTION IN A PLANE
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Position vectors can specify the location and
displacement of a point in an x-y coordinate
system

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Velocity In A Plane
vav (r2-r1) / (t2t1) ?r / ?t
Components of the average velocity
vectors are vav,x ?x / ?t and vav,y
?y / ?t



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At every point along the path, the instantaneous
velocity vector is tangent to the path.
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Independence Of Horizontal And Vertical Motions
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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 Earths rotation is ignored.
• The Earths curvature is ignored.

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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)
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Determination of key itemsfor projectiles

• x (vocos ?o)t
• ? tan-1(vy/vx)
• y (vosin ?o)t - ½gt2
• vx vocos?o
• vy vosin?o- gt

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• UNIFORM CIRCULAR MOTION

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Uniform Circular Motion



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Centripetal Acceleration arad v2/R
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• HOMEWORK
• 12, 17,22,36,

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• 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?