Honors S1w3 Flipped classroom Adding vectors

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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

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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

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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 $v=gt$

Obavezno

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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

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A man is running up and down his street. his displacement, velocity and acceleration is shown below. describe his run.

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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, slowing down at a constant rate. he then walks back to his front door. give a rough sketch of this on the position time graph below.

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how did you show that his velocity changed?

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how did you show his slowing down jog?

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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 both. do you have any questions?

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Review from the last lesson consider the following vectors

Stavka koja se može prevući		Odgovarajuća stavka
$\vec{u}\cdot\vec{v}$		the distance travelled
the magnitude of $\vec{u}$+ the magnitude of \$\vec{v}$ (this can also be written as \|\vec{u}\|+\|\vec{v}		the displacement
$\vec{u}+\vec{v}$		we have not done this yet, no.

Obavezno

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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 with the lab setting. What do you need to do in this scenario to subtract vectors?

Obavezno

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Who remembers basic trig from geometry?
If you know the magnitude (m) of a vector and its angle (θ) from the horizontal, which would you use to calculate the horizontal component of the vector?

m sin(θ)

m cos(θ)

m/sin(θ)

m/cos(θ)

Obavezno

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Any vector of magnitude m and angle θ can be written as the sum of two __________ vectors

opposite

parallel

perpendicular

resultant

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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 notice?

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A unit vector is a vector exactly 1 unit (whatever unit you are using) long in a specific direction. If it is going in the positive x direction it is written as shown below. It is read "i hat". the unit vector in the positive y direction would look like "j-hat".

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

Drugi mogući odgovor:

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

\hat{i}

\hat{j}

3\hat{j}

4\hat{i}

Obavezno

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which is the component way of describing vector 'a'

$44\hat{a}$

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

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if given a vector in component form, how would you find the magnitude of that vector?

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Play with the phet simulation with 2d vectors. create the situation show below. notice the horizontal and vertical components of the vectors and the resultant vector. play around with using tip to tail addition. give me the resultant \vec{a}+\vec{b} vector in component form. if you type in \hat in the math input, it will give you a box with a hat on top.

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add the vectors tip to tail

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Add the vectors in component form.

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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?

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

Stavka koja se može prevući		Odgovarajuća stavka
$\vec{boat}+\vec{river} = -10\hat{i}+4\hat{i}=-6\hat{i}$		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

Obavezno

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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?

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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

I've got this
i'm fuzzy
very confused

Honors 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, velocity and acceleration is shown below. describe his run.

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, slowing down at a constant rate. 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?

how did you show his slowing down jog?

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 both. do you have any questions?

Review from the last lesson consider the following vectors

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 with the lab setting. What do you need to do in this scenario to subtract vectors?

Who remembers basic trig from geometry? If you know the magnitude (m) of a vector and its angle (θ) from the horizontal, which would you use to calculate the horizontal component of the vector?

Any vector of magnitude m and angle θ can be written as the sum of two __________ vectors

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 notice?

which is the component way of describing vector 'a'

if given a vector in component form, how would you find the magnitude of that vector?

add the vectors tip to tail

Add the vectors in component form.

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, velocity and acceleration is shown below. describe his run.

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, slowing down at a constant rate. 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?

how did you show his slowing down jog?

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 both. do you have any questions?

Review from the last lesson consider the following vectors

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 with the lab setting. What do you need to do in this scenario to subtract vectors?

Who remembers basic trig from geometry? If you know the magnitude (m) of a vector and its angle (θ) from the horizontal, which would you use to calculate the horizontal component of the vector?

Any vector of magnitude m and angle θ can be written as the sum of two __________ vectors

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 notice?

which is the component way of describing vector 'a'

if given a vector in component form, how would you find the magnitude of that vector?

add the vectors tip to tail

Add the vectors in component form.

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?

Who remembers basic trig from geometry?
If you know the magnitude (m) of a vector and its angle (θ) from the horizontal, which would you use to calculate the horizontal component of the vector?

Who remembers basic trig from geometry?
If you know the magnitude (m) of a vector and its angle (θ) from the horizontal, which would you use to calculate the horizontal component of the vector?