{{asɛmtiNe Ɔkyerɛwfo}} | Nhomakorabea | Nneɛma a ɛma wotumi yɛ ade

Ɛhia

1

Review question: A man runs with a velocity of 10 mph, and then runs with a velocity of -10 mph. In simple terms this means

He runs forward, and then turns around and runs backwards

He runs forward and then turns around and runs in the opposite direction

He runs forward then turns left or right and continues in another direction

nothing. Negative velocity doesn't make sense

Ɛhia

1

Review question: A man runs with a speed of 10 mph, and then runs with a speed of -10 mph. In simple terms this means

He runs forward, and then turns around and runs backwards

He runs forward and then turns around and runs in the opposite direction

He runs forward then turns left or right and continues in another direction

nothing. Negative speed doesn't make sense

1

Plug and chug practice: The longer something falls, the faster its speed (in a vacuum). If a rock is dropped on the moon from a tower, and it takes 5 seconds to fall with the acceleration due to gravity being 1.6 $\frac{m}{{s}^{2}}$. Calculate how fast it is going when it hits the moon using the equation $v=gt$ you could read this equation as "velocity equals the acceleration due to gravity times the amount of time elapsed"

Ɛhia

1

If I drop two balls that are different masses, which one will land first, assuming no air resistance?

the heavy ball

the light ball

they should land at the same time

1

A man is running up and down his street. his displacement from his front door is shown on the graph above. explain his movement in words.

1

A man, starting at his front door he walks slowly up the street for 3 seconds, sprints for 4 seconds, then turns around and jogs for 6 seconds. he then walks back to his front door. give a rough sketch of this on the position time graph below.

1

how did you show that his velocity changed?

1

A man, starting at his front door he walks slowly up the street for 3 seconds going 2 meters per second. He then stays still for 10 seconds. sketch that on the graph.

1

We have been talking about vectors, now we need to talk about how to add and subtract them. There are two basic ways - geometric or algebraic. here is a video explaining geometric.
do you have any questions?

1

Review from the last lesson consider the following vectors

Draggable item		Corresponding Item
$\vec{u}+\vec{v}$		the distance travelled
$\vec{u}\cdot\vec{v}$		the displacement
the magnitude of $\vec{u}$+ the magnitude of \$\vec{v}$ (this can also be written as \|\vec{u}\|+\|\vec{v}		we have not done this yet, no.

1

add the following set of vectors. remember to redraw a vector so that the tip of one is at the tail of the next. then draw a line from the tail of the first to the tip of the second.

Ɛhia

1

Play with the phet simulation with 2d vectors. Create two vectors 'a' and 'b'. click the sum button to show the resultant vector of a+b. spend some time playing in the lab setting. What there is no option to subtract vectors, what can you do to be able to subtract vectors?

1

On the phet simulation, If I asked you to create a vector that has a magnitude of 15.3 and formed an angle (\theta) of 31.6 to the x-axis, could you do it?

yes

no

1

If you can add any two vectors to get a resultant vector, then you can describe any vector as the addition of two vectors, one going in the x direction and one going in the y direction. in the phet simulation, press the buttons under the word "components" in the top left. what do you see?

1

A unit vector is a vector with a magnitude of exactly 1 unit (whatever unit you are using) in a specific direction. If it is going in the positive x direction it is written as \hat{i} , which is read "i hat". the unit vector in the positive y direction would look like "j-hat".

sometimes we write vectors as being multiples of a unit vector, so the number shows the magnitude and the unit vector shows the direction.

Drag each written vector to the picture of the vector shown in the picture.

Mmuae Afoforo a Wobɛpaw:

\hat{i}

4\hat{i}

4\hat{i}+3\hat{j}

\hat{j}

3\hat{j}

Ɛhia

1

which is the component way of describing vector 'a'

$44\hat{a}$

$10\hat{i}+30\hat{j}$

Ɛhia

1

We call this decomposing a vector. to decomposed a vector is to write as the sum of two _____________ vectors

opposite

parallel

perpendicular

resultant

Ɛhia

1

Play with the phet simulation with 2d vectors. create the situation show below. What is the horizontal component of a?

5

10

15

20

Ɛhia

1

what is the horizontal component of b?

5

10

15

20

Ɛhia

1

what is the horizontal component of the sum of a+b

5

10

15

20

Ɛhia

1

Play with the simulation. press the 'sum' button to show the resultant vector a+b. rearrange the vectors like so. this is called the "tip to tail" method of vector addition. (if you want to use the phet simulation to check you work on problem 11, that is a good idea. How many of them did you get right?

Ɛhia

1

Turn on one of the "component views" like so. What is the relationship between the vertical components of a, b and s?

1

Adding vectors in their component form is a little like tallying up the dogs and cats in your neighborhood. House 1 has

5 cats+2 dogs
and house 2 has
1 cat +3 dogs.
we don't care how many animals there are, we believe in the strict segregation of dogs and cats ( 'cause my dog is terrified of cats) so we count the cats and dogs separately.

the two houses have 6 cats + 5 dogs

Vectors are the same - we add like to like.

if $\vec{u}=5\hat{i}+2\hat{j}$
and $\vec{p}=1\hat{i}+3\hat{j}$

then$\vec{u}+ \vec{p}=6\hat{i}+5\hat{j}$

try that out - if $\vec{n}=1\hat{i}+3\hat{j}$
and $\vec{m}=2\hat{m}+6\hat{j}$

find$\vec{n}+ \vec{m}$ = $\hat{m}$+$\hat{j}$

1

Adding vectors has a lot of applications in physics. It is useful for breaking 2 dimensional motion into two one-dimensional problems. we can also work with two separate factors to a situation. Consider a boat on a river. The boat is travelling at full power. on still water, this means 10 m/s. The water is fairly calm, and is traveling at 4 m/s. How fast is the boat moving with respect to the shore?

14 m/s

6 m/s

not enough information, what direction is the boat and river going?

1

in regards to the last problem, match the vector addition question to the situation

Draggable item		Corresponding Item
$\vec{boat}+\vec{river} = -10\hat{i}+4\hat{i}=-6\hat{i}$		the boat is moving in the same direction as the river
$\vec{boat}+\vec{river} = 4\hat{i}+10\hat{j}$		the boat is moving in the opposite direction as the river
$\vec{boat}+\vec{river} = 10\hat{i}+4\hat{i}=14\hat{i}$		the boat is trying to cross the river

Ɛhia

1

A plane is flying 300mph. a gust of wind picks up going the opposite direction of the plane at 60 mph. What is the new speed of the plane?

1

how are you feeling about this?

reading position time graphs and explaining the movement they represent
making my own position-time graphs
what is a vector
how to add vectors graphically
how to describe a vector using a horizontal vector added to a vertical vector
what is a unit vector
what are vector components
how to add vectors in component form
how to read a velocity-time graph
how are some ways we might use vectors?

I've got this
i'm fuzzy
very confused

S1w3 Flipped classroom Adding vectors

S1w3 Flipped classroom Adding vectors

Review question: A man runs with a velocity of 10 mph, and then runs with a velocity of -10 mph. In simple terms this means

Review question: A man runs with a speed of 10 mph, and then runs with a speed of -10 mph. In simple terms this means

If I drop two balls that are different masses, which one will land first, assuming no air resistance?

A man is running up and down his street. his displacement from his front door is shown on the graph above. explain his movement in words.

A man, starting at his front door he walks slowly up the street for 3 seconds, sprints for 4 seconds, then turns around and jogs for 6 seconds. he then walks back to his front door. give a rough sketch of this on the position time graph below.

how did you show that his velocity changed?

A man, starting at his front door he walks slowly up the street for 3 seconds going 2 meters per second. He then stays still for 10 seconds. sketch that on the graph.

We have been talking about vectors, now we need to talk about how to add and subtract them. There are two basic ways - geometric or algebraic. here is a video explaining geometric. do you have any questions?

Review from the last lesson consider the following vectors

add the following set of vectors. remember to redraw a vector so that the tip of one is at the tail of the next. then draw a line from the tail of the first to the tip of the second.

Play with the phet simulation with 2d vectors. Create two vectors 'a' and 'b'. click the sum button to show the resultant vector of a+b. spend some time playing in the lab setting. What there is no option to subtract vectors, what can you do to be able to subtract vectors?

On the phet simulation, If I asked you to create a vector that has a magnitude of 15.3 and formed an angle (\theta) of 31.6 to the x-axis, could you do it?

If you can add any two vectors to get a resultant vector, then you can describe any vector as the addition of two vectors, one going in the x direction and one going in the y direction. in the phet simulation, press the buttons under the word "components" in the top left. what do you see?

which is the component way of describing vector 'a'

We call this decomposing a vector. to decomposed a vector is to write as the sum of two _____________ vectors

Play with the phet simulation with 2d vectors. create the situation show below. What is the horizontal component of a?

what is the horizontal component of b?

what is the horizontal component of the sum of a+b

Turn on one of the "component views" like so. What is the relationship between the vertical components of a, b and s?

in regards to the last problem, match the vector addition question to the situation

A plane is flying 300mph. a gust of wind picks up going the opposite direction of the plane at 60 mph. What is the new speed of the plane?

how are you feeling about this?

Review question: A man runs with a velocity of 10 mph, and then runs with a velocity of -10 mph. In simple terms this means

Review question: A man runs with a speed of 10 mph, and then runs with a speed of -10 mph. In simple terms this means

If I drop two balls that are different masses, which one will land first, assuming no air resistance?

A man is running up and down his street. his displacement from his front door is shown on the graph above. explain his movement in words.

A man, starting at his front door he walks slowly up the street for 3 seconds, sprints for 4 seconds, then turns around and jogs for 6 seconds. he then walks back to his front door. give a rough sketch of this on the position time graph below.

how did you show that his velocity changed?

A man, starting at his front door he walks slowly up the street for 3 seconds going 2 meters per second. He then stays still for 10 seconds. sketch that on the graph.

We have been talking about vectors, now we need to talk about how to add and subtract them. There are two basic ways - geometric or algebraic. here is a video explaining geometric. do you have any questions?

Review from the last lesson consider the following vectors

add the following set of vectors. remember to redraw a vector so that the tip of one is at the tail of the next. then draw a line from the tail of the first to the tip of the second.

Play with the phet simulation with 2d vectors. Create two vectors 'a' and 'b'. click the sum button to show the resultant vector of a+b. spend some time playing in the lab setting. What there is no option to subtract vectors, what can you do to be able to subtract vectors?

On the phet simulation, If I asked you to create a vector that has a magnitude of 15.3 and formed an angle (\theta) of 31.6 to the x-axis, could you do it?

If you can add any two vectors to get a resultant vector, then you can describe any vector as the addition of two vectors, one going in the x direction and one going in the y direction. in the phet simulation, press the buttons under the word "components" in the top left. what do you see?

which is the component way of describing vector 'a'

We call this decomposing a vector. to decomposed a vector is to write as the sum of two _____________ vectors

Play with the phet simulation with 2d vectors. create the situation show below. What is the horizontal component of a?

what is the horizontal component of b?

what is the horizontal component of the sum of a+b

Turn on one of the "component views" like so. What is the relationship between the vertical components of a, b and s?

in regards to the last problem, match the vector addition question to the situation

A plane is flying 300mph. a gust of wind picks up going the opposite direction of the plane at 60 mph. What is the new speed of the plane?

how are you feeling about this?

We have been talking about vectors, now we need to talk about how to add and subtract them. There are two basic ways - geometric or algebraic. here is a video explaining geometric.
do you have any questions?

We have been talking about vectors, now we need to talk about how to add and subtract them. There are two basic ways - geometric or algebraic. here is a video explaining geometric.
do you have any questions?