S11 A squirrel shoots his machine gun at

SP 1. Students will analyze the relationships between force, mass, gravity, and the motion

Scalar – number with units (magnitude) Vector – has both magnitude and direction displacement

2. 2 The Components of a Vector Compare and contrast scalar and vector quantities.

Vectors can be broken down into components A fancy way of saying how far

We calculate the sides using trig 2. 2 The Components of a Vector Compare

A represents any vector 2. 2 The Components of a Vector Compare and contrast

Then we can calculate the y 2. 2 The Components of a Vector Compare

For example if a vector that is 45 m @ 25 o 2. 2

Practice Components of Vectors Compare and contrast scalar and vector quantities.

If we know the components you can calculate the original the value of the

The direction is given as an angle from the +x axis Positive is counterclockwise

Practice Resolving Vectors Compare and contrast scalar and vector quantities.

2. 3 Adding and Subtracting Vectors Compare and contrast scalar and vector quantities.

Always make a sketch of vector addition so you can approximate the correct answer

2. Break vectors into their components 3. Add the components to calculate the components

When vectors are subtracted 1. The vector being subtracted has its direction changed by

Practice Adding and Subtracting Vectors Compare and contrast scalar and vector quantities.

S-12 A moose is trying out his new advanced attack shuttle to hunt down

Projectile Motion – object traveling through space under the influence of only gravity From

Acceleration is caused by gravity In what axis? Only in the y What happens

So if there is no gravity 2. 4 Motion in Two Dimensions Measure and

In the y axis, acceleration is always -9. 80 m/s 2 All the acceleration

The actual pathway has constant x velocity and changing y Acceleration in the -y

2. 5 Projectile Motion: Basic Equations Measure and calculate two-dimensional motion by using component

We will assume no air resistance gravity is 9. 80 m/s 2 That leaves

The two axis are independent of each other except for time X Y vx

2. 6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

If an object is launched at 0 o vx = vcosq = v vy

Now we can fill in whatever else is given in the problem X Y

A person on a skate board with a constant speed of 1. 3 m/s

We are now prepared to answer some questions A) How long is the ball

We are no prepared to answer some questions A) How long is the ball

Basically a one dimensional problem Notice that time is the same in both the

We can now solve for X variable if we want B) What is the

Practice Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

S-13 A pig is tied to a rocket and shot upward with an acceleration

2. 7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

All that changes if the launch angle is not zero vx = vcosq vy

Example: A projectile is launched with an initial speed of 20 m/s at an

Practice General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

S-14 The Blue Aardvark throws an ant off a tall hill. If the ant

Practice Measure and calculate two-dimensional motion by using component vectors.

A-15 A gopher is out worshipping the sun god, when a bird swoops down

A-16 A dancing 2000 kg hippo leaps gracefully into the air. If she reaches

S-17 A killer tomato leaps at an unsuspecting dancing lady. If the tomato jumps

S-18 A really cute bunny is tossed by his friends over a fence to

S-19 Dude is out jumping his windsurfer dude, when he catches a really cool

S-20 Three Giraffes named Ira, Samuel, and Lissette are singing a happy song when

S-21 A wolf named Sam is doing his best victory dance because his mom

S-22 Kermit “Baby Face” Frog shoots his AK-47 at an angle of 37 o.

S-23 A little song for your testing enjoyment Oh Happy Test Day Sorrow and

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S-11 A squirrel shoots his machine gun at the evil bunny family across the street. If the bullet starts from rest and exits the barrel at 1000 m/s, what is the acceleration of the bullet. Assume that the barrel is. 35 m long.

Unit 2 V e c t o r s

2. 1 Scalars Versus Vectors

SP 1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. b. Compare and contrast scalar and vector quantities. Standard

Scalar – number with units (magnitude) Vector – has both magnitude and direction displacement velocity acceleration Vector notation – letter with arrow 2. 1 Scalars Versus Vectors Compare and contrast scalar and vector quantities.

2. 2 The Components of a Vector Compare and contrast scalar and vector quantities.

Vectors can be broken down into components A fancy way of saying how far it goes on the x and on the y 2. 2 The Components of a Vector Compare and contrast scalar and vector quantities.

We calculate the sides using trig 2. 2 The Components of a Vector Compare and contrast scalar and vector quantities.

A represents any vector 2. 2 The Components of a Vector Compare and contrast scalar and vector quantities.

Then we can calculate the y 2. 2 The Components of a Vector Compare and contrast scalar and vector quantities.

For example if a vector that is 45 m @ 25 o 2. 2 The Components of a Vector Compare and contrast scalar and vector quantities.

Practice Components of Vectors Compare and contrast scalar and vector quantities.

If we know the components you can calculate the original the value of the vector. Magnitude is calculated using the Pythagorean theorem 2. 2 The Components of a Vector Compare and contrast scalar and vector quantities.

The direction is given as an angle from the +x axis Positive is counterclockwise 2. 2 The Components of a Vector Compare and contrast scalar and vector quantities.

Practice Resolving Vectors Compare and contrast scalar and vector quantities.

2. 3 Adding and Subtracting Vectors Compare and contrast scalar and vector quantities.

Always make a sketch of vector addition so you can approximate the correct answer Vector Addition Applet Steps in vector addition 1. Sketch the vector 2. a. Head to tail method 3. b. Parallelogram method 2. 3 Adding and Subtracting Vectors Compare and contrast scalar and vector quantities.

2. Break vectors into their components 3. Add the components to calculate the components of the resultant vector 4. Calculate the magnitude of R 5. Calculate the direction of R 6. a. Add 180 o to q if Rx is negative 2. 3 Adding and Subtracting Vectors Compare and contrast scalar and vector quantities.

2. 3 Adding and Subtracting Vectors Compare and contrast scalar and vector quantities.

When vectors are subtracted 1. The vector being subtracted has its direction changed by 180 o 2. Then we follow the steps of vector addition 2. 3 Adding and Subtracting Vectors Compare and contrast scalar and vector quantities.

Practice Adding and Subtracting Vectors Compare and contrast scalar and vector quantities.

S-12 A moose is trying out his new advanced attack shuttle to hunt down defenseless baby deer. He travels north for 100 m, then goes 120 m @ 25 o, and finally turns and goes 211 m @ -309 o. What is his displacement?

2. 4 Motion in Two Dimensions

SP 1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. f. Measure and calculate twodimensional motion (projectile and circular) by using component vectors. Standard

Projectile Motion – object traveling through space under the influence of only gravity From the moment it is launched until the instant before it hits the ground 2. 4 Motion in Two Dimensions Measure and calculate two-dimensional motion by using component vectors.

Acceleration is caused by gravity In what axis? Only in the y What happens in the x? Constant velocity 2. 4 Motion in Two Dimensions Measure and calculate two-dimensional motion by using component vectors.

So if there is no gravity 2. 4 Motion in Two Dimensions Measure and calculate two-dimensional motion by using component vectors.

In the y axis, acceleration is always -9. 80 m/s 2 All the acceleration equations apply In the y axis motion is identical to falling 2. 4 Motion in Two Dimensions Measure and calculate two-dimensional motion by using component vectors.

The actual pathway has constant x velocity and changing y Acceleration in the -y Projectile 2. 4 Motion in Two Dimensions Measure and calculate two-dimensional motion by using component vectors.

2. 5 Projectile Motion: Basic Equations Measure and calculate two-dimensional motion by using component vectors.

We will assume no air resistance gravity is 9. 80 m/s 2 That leaves the following variables X Y vx = voy = x= vy = t= t= the Earth is a = -9. 80 m/s not moving y= (Frame of Reference) 2. 5 Projectile Motion: Basic Equations 2 Measure and calculate two-dimensional motion by using component vectors.

The two axis are independent of each other except for time X Y vx = voy = x= vy = t= t= a = -9. 80 m/s 2 y= 2. 5 Projectile Motion: Basic Equations Measure and calculate two-dimensional motion by using component vectors.

2. 6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

If an object is launched at 0 o vx = vcosq = v vy = vsinq = 0 So our chart becomes X Y vx = v voy = 0 x= vy = t= t= a = -9. 80 m/s 2 y= 2. 6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

Now we can fill in whatever else is given in the problem X Y vx = v voy = 0 x= vy = t= t= a = -9. 80 m/s 2 y= 2. 6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

A person on a skate board with a constant speed of 1. 3 m/s releases a ball from a height of 1. 25 m above the ground. What variable can you fill in? X Y vx = v voy = 0 x= vy = t= t= a = -9. 80 m/s 2 y= 2. 6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

A person on a skate board with a constant speed of 1. 3 m/s releases a ball from a height of 1. 25 m above the ground. What variable can you fill in? X Y vx = 1. 3 m/s voy = 0 x= vy = t= t= a = -9. 80 m/s 2 y = -1. 25 m 2. 6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

We are now prepared to answer some questions A) How long is the ball in the air? X Y vx = 1. 3 m/s voy = 0 x= vy = t= t= a = -9. 80 m/s 2 y = -1. 25 m 2. 6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

We are no prepared to answer some questions A) How long is the ball in the air? X Y vx = 1. 3 m/s voy = 0 x= vy = t = 0. 505 s a = -9. 80 m/s 2 y = -1. 25 m 2. 6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

Basically a one dimensional problem Notice that time is the same in both the Y and the X X Y vx = 1. 3 m/s voy = 0 x= vy = t = 0. 505 s a = -9. 80 m/s 2 y = -1. 25 m 2. 6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

We can now solve for X variable if we want B) What is the x displacement? X Y vx = 1. 3 m/s voy = 0 x= vy = t = 0. 505 s a = -9. 80 m/s 2 y = -1. 25 m 2. 6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

We can now solve for X variable if we want B) What is the x displacement? X Y vx = 1. 3 m/s voy = 0 x =0. 656 m vy = t = 0. 505 s a = -9. 80 m/s 2 y = -1. 25 m 2. 6 Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

Practice Zero Launch Angle Measure and calculate two-dimensional motion by using component vectors.

S-13 A pig is tied to a rocket and shot upward with an acceleration of 5 m/s 2 at an angle of 35 o. After 4 seconds, what is the x and y component of his velocity?

2. 7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

All that changes if the launch angle is not zero vx = vcosq vy = vsinq X Y vx = voy = x= vy = t= t= a = -9. 80 m/s 2 y= 2. 7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35 o. What is displacement after 1. 00 s? X Y vx = voy = x= vy = t = 1. 00 s a = -9. 80 m/s 2 y= 2. 7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35 o. What is displacement after 1. 00 s? vx = vcosq =20 cos 35 vx = 16. 4 m/s X Y vx = voy = x= vy = t = 1. 00 s a = -9. 80 m/s 2 y= 2. 7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35 o. What is displacement after 1. 00 s? vx = vcosq =20 cos 35 vx = 16. 4 m/s X Y vx = 16. 4 m/s voy = x= vy = t = 1. 00 s a = -9. 80 m/s 2 y= 2. 7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35 o. What is displacement after 1. 00 s? vy = vsinq = 20 sin 35 vx = 11. 5 m/s X Y vx = 16. 4 m/s voy = x= vy = t = 1. 00 s a = -9. 80 m/s 2 y= 2. 7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35 o. What is displacement after 1. 00 s? vy = vsinq = 20 sin 35 vx = 11. 5 m/s X Y vx = 16. 4 m/s voy = 11. 5 m/s x= vy = t = 1. 00 s a = -9. 80 m/s 2 y= 2. 7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35 o. What is displacement after 1. 00 s? x = vt x = (16. 4)(1) = 16. 4 X Y vx = 16. 4 m/s voy = 11. 5 m/s x= vy = t = 1. 00 s a = -9. 80 m/s 2 y= 2. 7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35 o. What is displacement after 1. 00 s? x = vt x = (16. 4)(1) = 16. 4 X Y vx = 16. 4 m/s voy = 11. 5 m/s x = 16. 4 m vy = t = 1. 00 s a = -9. 80 m/s 2 y= 2. 7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35 o. What is displacement after 1. 00 s? y=voyt+½at 2 y=11. 5(1)+½(-9. 8)(1)2 y=6. 6 m X Y vx = 16. 4 m/s voy = 11. 5 m/s x = 16. 4 m vy = t = 1. 00 s a = -9. 80 m/s 2 y= 2. 7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35 o. What is displacement after 1. 00 s? displacement (magnitude) X Y vx = 16. 4 m/s voy = 11. 5 m/s x = 16. 4 m vy = t = 1. 00 s a = -9. 80 m/s 2 y = 6. 6 m 2. 7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35 o. What is displacement after 1. 00 s? displacement (magnitude) = 17. 7 m direction X Y vx = 16. 4 m/s voy = 11. 5 m/s x = 16. 4 m vy = t = 1. 00 s a = -9. 80 m/s 2 y = 6. 6 m 2. 7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

Practice General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

S-14 The Blue Aardvark throws an ant off a tall hill. If the ant is thrown 55 m/s @ 22 o, what is the maximum height that he reaches?