Vectors!!!

Review: Vectors and Scalars

Vectors have:

Magnitude

Unit

Direction

Scalars have:

Number

Unit

Big point to remember.

the magnitude of a vector is ALWAYS positive

the direction can be negative however.

You will learn to recognize the vectors in your

book as letters with an arrow over the top of them.

The magnitude of the vector will NOT

have an arrow.

Which of these CANNOT be a

magnitude of a vector

A. 10 m

B. 12 m/s

C. -4 N

D. 78 yrd

Which of these magnitudes is

actually just a scalar (look at units)

A. 30 m

B. 27 s

C. 15 N

D. 89 m/s^2

Vectors graphically

A vector is a magnitude and direction

Are these two vectors

the same?

How about these two?

Adding Vectors graphically

A

B

Tail-to-tip method

A

B

A

B

C

C = A + B

What about C = A-B ?

A

B

A

B

A

B

C

C = A - B

A bit to note:

When is this true

Another special case

A

B

C

Pythagorean theorem

**THIS IS KEY**

What must we have for Pythagorean theorem to work?

Two vectors at right angles or simply a right triangle

What does it relate?

the MAGNITUDE of all 3 sides

Y

X

V

V

y

x

O

O

O

Hypotenuse

Opposite side

Adjacent side

O

5

4

3

y

V

y

V

x

V

V

Sin =

Tan =

O

O

O

V

x

V

O

y

V

X

X = 2 V

W = - X

X

W

Multiply by a Scalar

"Gravity is a force that explains objects with mass attracting towards each other? Like Planets orbiting around the sun. Why don't things orbit on earth?"

"Can you go over how the parallelogram rule for adding vectors works? That was a bit confusing for me."

"Can you go over example 3.2 on page 73?"

" How is displacement direction aware and distance is not?"

"Can we review how to use the law of cosines to solve vector additions?"

"Why must vectors be used? Is there an easier way to do this?"

"Rocket problem !!!!"

Ball bearings are made by letting spherical drops of molten metal fall inside a tall tower - called a shot tower - and solidify as they fall

a. If a bearing needs 4.0 s to solidify enough for impact, how high must the tower be?

b. What is the bearing's impact velocity?

A student standing on the ground throws a ball straight up. The ball leaves the student's hand with a speed of 15 m/s when the hand is 2.0 m above the ground. How long is the ball in the air before it hits the ground? ( the student moves her hand out of the way.)

78 m

39.2 m/s

3.19 s

The position of a particle is given by the function

x = 2t -9t +12

a. At what time or times is v = 0 m/s

b. What are the particle's position and its acceleration at this time(s) ?

3

2

x

v = 6 t -18t

2

t = 0, 3 s

x = 12 , -15 m

a = 12 t -18

a = -18 18 m/s

2

A particle's velocity is described by the function

v = t -7t + 10 m/s.

a. At what times does the particle reach its turning points?

b. What is the particles acceleration at each of the turning points?

2

x

t = 2 , 5 s

a = - 3, 3 m/s

2