Download Vectors and 2D motion and more Slides Physics in PDF only on Docsity!

3: Vectors

So far we have been focusing on only one

dimension.

Before getting to two and three dimensions we

want to need to review vectors in two and three

dimensions.

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

Graphically adding/subtracting vectors

gives you a qualitative answer

Subtracting Vectors

Subtract the following two vectors

v=(v

f

• v

):i

v

f

+ (-v

) =i

v

v f v f

A B C D E Which figure shows A - B A B C D E 86% 0% 0% 0% 14%

A

B

C

D

E

Initial response(s)

Correctresponse 9

A B C D E Which figure shows 2A - B A B C D E 93% 0% 7% 0% 0%

A

B

C

D

E

Initial response(s)

Correctresponse 9

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 =

adj hyp

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

• Clicker Question Sequence: Vectors
• Clicker Question Sequence: Vectors

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)

Correctresponse 9

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