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Vectors: the goals • Be able to define the term VECTOR and identify quantities which are vectors. • Be able to add vectors by the “Head to Tail Method” • Be able to use the idea of vectors to solve problems in physics.

Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

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Page 1: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Vectors: the goals

• Be able to define the term VECTOR and identify quantities which are vectors.

• Be able to add vectors by the “Head to Tail Method”

• Be able to use the idea of vectors to solve problems in physics.

Page 2: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Vectors: the goals

• Understand that VECTORS are to be used in describing situations that involve FORCES and VELOCITIES.

• Understand that VECTORS will be used again when we discuss Gravitational, Electric, and Magnetic Force fields

Page 3: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

What is a vector?

A

B

Page 4: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

What is a vector?

A

B

Which Ball is moving the fastest?

Page 5: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

What is a vector?

A

B

Page 6: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

What is a vector?

A

B

Now try again…

Which ball is moving faster?

Page 7: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

What is a vector?

A

B

Now try again…

Which ball is moving faster?

Could we say that “A” is moving twice as fast as “B”? How could we justify that?

Page 8: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Vectors

A vector is any quantity that has a direction as well as an amount.

Page 9: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Definition of a vector:

• A vector is anything that has direction and value.

• Examples are: force, velocity, acceleration, momentum.

• Things which are NOT vectors such as mass, area, volume, are called scalars.

Page 10: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Using Vectors to solve a problem:

Page 11: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Using Vectors to solve a problem:

Page 12: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Using Vectors to solve a problem:

Vtrain= 10 m/s

Vman= 3 m/s

Page 13: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Using Vectors to solve a problem:

Vtrain= 10 m/s

Vman= 3 m/s

How fast is the man moving with respect to the ground? Which direction?

Page 14: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Adding vectors to get an answerDraw the first vector. Be sure to leave the length and direction exactly as it was.

Page 15: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Adding vectors to get an answerDraw the second vector. Be sure to leave the length and direction exactly as it was, and draw the second vector with its tail on the head of the first.

Page 16: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Adding vectors to get an answerThe answer is called the RESULTANT. The answer is drawn from the tail of the first vector to the head of the last vector.

Page 17: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Adding vectors to get an answerMeasure the length of the RESULTANT vector. In this case, the answer will be 7 m/s to the right.

Page 18: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Using Vectors to solve a problem:

Vtrain= 10 m/s

Vman= 3 m/s

Now, how fast is the man moving with respect to the ground? In which direction?

Page 19: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Adding vectors to get an answerDraw the first vector. Be sure to leave the length and direction exactly as it was.

Page 20: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Adding vectors to get an answerDraw the second vector. Be sure to leave the length and direction exactly as it was, and draw the second vector with its tail on the head of the first.

Page 21: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Adding vectors to get an answerMeasure the length of the RESULTANT vector. In this case, the answer will be 13 m/s to the right.

Page 22: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Using Vectors to solve a problem:

• What if the railroad car is moving at 10 m/s as before.

• The man on the car is walking at 3 m/s toward the side of the car.

• What will be the velocity of the man with respect to the ground?

Page 23: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Using Vectors to solve a problem:

Page 24: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Using Vectors to solve a problem:

Draw the vectors Head to tail:

Page 25: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Using Vectors to solve a problem:

Draw the vectors Head to tail:

And then draw the RESULTANT fromThe Tail of the First to the Head of the Last.

Page 26: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Using Vectors to solve a problem:

Draw the vectors Head to tail:

And then draw the RESULTANT fromThe Tail of the First to the Head of the Last.

Try this yourself and tell me what you get as an answer.

Page 27: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Using Vectors to solve a problem:

Draw the vectors Head to tail:

And then draw the RESULTANT fromThe Tail of the First to the Head of the Last.

The answer is 10.44 m/s at 17.5o from the first vector.

Page 28: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Using Vectors to solve a problem:

• What if the railroad car is moving at 10 m/s as before to the East.

• There is a second car on top of the first moving South at 5 m/s

• The man is on the top car walking at 3 m/s to the Southwest

• What will be the velocity of the man with respect to the ground?

Page 29: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Using Vectors to solve a problem:

Page 30: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Using Vectors to solve a problem:

Page 31: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Using Vectors to solve a problem:

Page 32: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

Using Vectors to solve a problem:

The answer is: 10.5 m/s at an angle of 42.5 degrees south of East.

Page 33: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

The Boat Problem

A B

Page 34: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

The Boat Problem

A B

Vboat= 12 m/s

Page 35: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

The Boat Problem

A B

Vboat= 12 m/s

Vriver= 5 m/s

Page 36: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

The Boat Problem

A B

Vboat= 12 m/s

Vriver= 5 m/s

Distance = 360 meters

Page 37: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

The Boat Problem

A B

What will the actual velocity of the boat be (find both speed and direction)?

How long will it take to cross the river?

Where will the boat land (how far downstream from point “B” will the boat land?)

Page 38: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

The Boat Problem

A B

Vboat= 12 m/s

Vriver= 5 m/s

Page 39: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

The Boat Problem

A BVboat= 12 m/s

Vriver= 5 m/sDraw the vectors head to tail.

Page 40: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

The Boat Problem

A BVboat= 12 m/s

Vriver= 5 m/s

Page 41: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

The Boat Problem

A BVboat= 12 m/s

Vriver= 5 m/sVactual=13 m/s @22.6o

Page 42: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

The Boat Problem

A B

Vboat= 12 m/s

Vriver= 5 m/s

Distance = 360 meters

Page 43: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

The Boat Problem

A B

Vboat= 12 m/s

Vriver= 5 m/s

Distance = 360 meters

What angle must the pilot use in order to cross the river straight, and land at point B?

Page 44: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

The Boat Problem

A B

Vboat= 12 m/sVriver= 5 m/s

The solution to this problem has to be constructed differently.

Page 45: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

The Boat Problem

Vboat= 12 m/sVriver= 5 m/s

Draw the River velocity vector first.

Page 46: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

The Boat Problem

Vboat= 12 m/sVriver= 5 m/s

Draw a line in the direction of the answer you want.

The Head of the RESULTANT will be on the head of the Vriver.

Page 47: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

The Boat Problem

Vboat= 12 m/s

Vriver= 5 m/s

The Head of the RESULTANT will be on the head of the Vriver.

Rotate and fit in the 12 cm long vector into the only place it will fit. This will define where the Vactual vector will be.

Page 48: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

The Boat Problem

Vboat= 12 m/s

Vriver= 5 m/s

The Head of the RESULTANT will be on the head of the Vriver.

Rotate and fit in the 12 cm long vector into the only place it will fit. This will define where the Vactual vector will be.

Vactual

Page 49: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

The Boat Problem

A B

What will the actual velocity of the boat be?

What angle must be used to head the boat?

How long will it take to cross the river?

Page 50: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

The Boat Problem

Vboat= 12 m/s

Vriver= 5 m/s

Vactual= 10.9 m/s

Angle=24.6o

Page 51: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

The Boat Problem

A B

Vboat= 12 m/s

Vriver= 5 m/s

Distance = 360 meters

Vactual=10.9 m/s

Page 52: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

The Boat Problem

A B

Vboat= 12 m/s

Vriver= 5 m/s

Distance = 360 meters

Vactual=10.9 m/s

The time to get across will be 360m/10.9 m/s =33 seconds

Page 53: Vectors: the goals Be able to define the term VECTOR and identify quantities which are vectors. Be able to add vectors by the “Head to Tail Method” Be

The Boat Problem

A B

Vboat= 12 m/s

Vriver= 5 m/s

Distance = 360 meters

Vactual=10.9 m/s

…and the boat winds up straight across the river at point B


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