Vectors and Dynamics

7/30/2019 Vectors and Dynamics

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Blank page!

This page deliberately left pseudo-blank.
http://find/


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Clicker Question 1:

What are the x- and y-components of the

following vector?A. 3, -1

B. 3, -4C. 4, 3

D. 4, -3

E. -3, -4
http://goforward/http://find/http://goback/


3/14

Clicker Question 1:

What are the x- and y-components of the

following vector?A. 3, -1

B. 3, -4

C. 4, 3

D. 4, -3

E. -3, -4
http://find/


4/14

Clicker Question 2:

The following vector has length 4.0 units. What

are the x- and y-components?

A. 3.5, 2.0

B. -3.5, 2.0

C. -2.0, 3.5

D. 2.0, -3.5

E. -3.5, -2.0
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5/14

Clicker Question 2:

The following vector has length 4.0 units. What

are the x- and y-components?

A. 3.5, 2.0

B. -3.5, 2.0

C. -2.0, 3.5

D. 2.0, -3.5

E. -3.5, -2.0
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Vector components example 1.0:

The following vectors have length 3.0 units. For

each vector, what is the component parallel to theramp surface?
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Vector components example 1.5:

The following vectors have length 3.0 units. For

each vector, what is the component perpendicularto the ramp?
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Example EXTREME! (Part 1):

A new ski area emphasizes the extreme skiingpossible on its slopes. Suppose one of the ads

says, Free-fall skydiving is the greatest rush you

can experience. . . but well take you as close asyou can get on land. When you tip your skis down

the slope of our steepest runs, you can accelerate

at up to 75% of the acceleration youd experiencein free fall.

What angle slope could give such an acceleration?
http://goforward/http://find/http://goback/


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A new ski area emphasizes the extreme skiing

possible on its slopes. Suppose one of the adssays, Free-fall skydiving is the greatest rush you

can experience. . . but well take you as close as

you can get on land. When you tip your skis downthe slope of our steepest runs, you can accelerate

at up to 75% of the acceleration youd experience

in free fall.

What angle slope could give such an acceleration?49
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10/14


Given such an acceleration (75% ofg parallel to

the slope), how long would it take a skier to makeit 400 meters down the slope, from rest?
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11/14


Given such an acceleration (75% ofg parallel tothe slope), how long would it take a skier to make

it 400 meters down the slope, from rest?

x(t) = x0 +v0 t+1

2

0.75 9.80m/s2

t2

= 400m = 0 + 0 + 389.80m/s2 t2

= t=

400m

3.675m/s2 10.4 s .
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Example EXTREME! Quick Answer!:

Suppose you skydive (or base-jump, or something)

400 m, instead. How long would it take you to

simply fall 400 m, as a proportion of the time wefound for the skier? In other words, what is

timefreefalltimeski

?
http://find/


13/14

Example EXTREME! Quick Answer!:

Suppose you skydive (or base-jump, or something)

400 m, instead. How long would it take you tosimply fall 400 m, as a proportion of the time we

found for the skier? In other words, what istimefreefalltimeski ?xfall =

1

2gt

2

fall

xski =

1

2

3

4gt2

ski

= 34

xfall

xski=

t2fall

t2ski

=tfall

tski =3

4 =

3

2 0.87

.
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Quiz:The figure shows a skier at the bottom of his ski slope, at twodifferent moments in time, along with the his velocity vector at each

of those times. The time incrementt

is very small, so that thevelocity v2 at time t2 = t1+t is measured very soon after thevelocity v1.Given the definition for average acceleration, a v

t, or

instantaneous acceleration, a

dv

dt, in which direction does the

acceleration vector point for the skier?

A. from the skier to thecenter of the circle

B. parallel to v2

C. straight down

D. opposite (antiparallel) to v1
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