Ch 10.2 Vectors in the Plane

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Ch 10.2 Vectors in the Plane

• Calculus Graphical, Numerical, Algebraic by
• Finney, Demana, Waits, Kennedy

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The component form of vector v is
lt 2 cos 60º, 2 sin 60ºgt
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Unit Vector is or lt cos ?, sin ? gt
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Vector Addition
Two ways to represent vector addition
geometrically a) tail-to-head b)
parallelogram representation
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N
50
60º
E
400
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Doing Calculus Componentwise

• A particle moves in the plane so that its
  position at any time t 0 is given by (sin t,
  t2/2).
• Find the position vector of the particle at time
  t
• Find the velocity vector of the particle at time
  t
• Find the acceleration of the particle at time t.
• Describe the position and motion of the particle
  at time t 6.

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Doing Calculus Componentwise

• A particle moves in the plane so that its
  position at any time t 0 is given by (sin t,
  t2/2).
• Find the position vector of the particle at time
  t.
• The position vector, which has the same
  components as the position point is lt sin t, t2/2
  gt.
• b) Find the velocity vector of the particle at
  time t.
• Differentiate each component of the velocity
  vector to get lt cos t, t gt.
• Find the acceleration of the particle at time t.
• Differentiate each component of the
  acceleration vector to get lt -sin t, 1 gt.
• Describe the position and motion of the particle
  at time t 6.
• The particle is at the point (sin 6, 18) with
  velocity lt cos 6, 6 gt and acceleration lt -sin 6,
  1 gt.

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Studying Planar Motion
A particle moves in the plane with position
vector r(t) lt sin (3t), cos (5t) gt. Find the
velocity and acceleration vectors and determine
the path of the particle.
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Studying Planar Motion
A particle moves in the plane with position
vector r(t) lt sin (3t), cos (5t) gt. Find the
velocity and acceleration vectors and determine
the path of the particle. Velocity v(t) lt 3
cos (3t), -5 sin (5t) gt Acceleration a(t) lt -9
sin (36), -25 cos (5t) gt The path of the
particle is found by graphing the curve and using
path.
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