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Concepts of vector quantities as they relate to motion.
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Vectors Method of Adding and Subtracting vectors in 1D we started thinking about vectors and adding and subtracting them Recall: head-tail method for adding vectors
draw the first vector - draw the second vector with its tail starting at the head of thefirst.^ the resultant vector is the vector drawn from the tail of the first vector to the head of the second vector. Also called the triangle method
Subtracting Vectors
f
f
v f v f
A B C D E Which figure shows A - B A B C D E 86% 0% 0% 0% 14%
Initial response(s)
A B C D E Which figure shows 2A - B A B C D E 93% 0% 7% 0% 0%
Initial response(s)
Resolving Vectors into Components v v v y x v v v =
x y v y v x θ Any vector in x, y planecan be broken up into x and y components Practice Questions (break these vectors into x and y components) x y x y
Resolving Vectors into Components v v v y x v v v =
cos x y v y v x θ Any vector in x, y planecan be broken up into x and y components vx^ v =
cos x v v =
cos Find the x and y component Right Triangle Æ can use trig to figure this out x-component opp^ hyp =
sin vy^ v =
sin y v v =
sin y-component
N S E W
If I travel 5 miles east and then 2 miles west. What would my displacement vector look like? (Each box represents 1 mile.) Arrow 1 Arrow 2 Arrow 3 Arrow 4 Arrow 5 Arrow 6 21% 7% 7% 0% 7% 57%
Arrow 1
Arrow 2
Arrow 3
Arrow 4
Arrow 5
Arrow 6 Initial response(s)
Practice Problem Suppose a velocity vector has a component in the – y directionof 4 m/s and a component in the x direction of 3 m/s. Sketch the vector at right. Determine the angle at which the object is launched Determine the magnitude of the velocity vector y v x v = θ tan v y v x v θ ( ) y v x v 1 tan − = θ ( ) 2 2 y x v v v
=
Unit Vectors in 3-D ⇒^ ⇒ ⇒ k j i ˆ^ ˆ ˆ Unit vector in +xdirection Unit vector in +ydirection Unit vector in +zdirection