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.

Vec t o r s Unit 2

2.1 Scalars Versus Vectors

b. Compare and contrast scalar and vector quantities. SP1. 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 @ 25o 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.

Magnitude is calculated using the Pythagorean theorem 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.

Steps in vector addition Sketch the vector a. Head to tail method Always make a sketch of vector addition so you can approximate the correct answer Vector Addition Applet Steps in vector addition Sketch the vector a. Head to tail method b. Parallelogram method 2.3 Adding and Subtracting Vectors Compare and contrast scalar and vector quantities.

Compare and contrast scalar and vector quantities. Break vectors into their components Add the components to calculate the components of the resultant vector Calculate the magnitude of R Calculate the direction of R a. Add 180o 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.

Compare and contrast scalar and vector quantities. When vectors are subtracted The vector being subtracted has its direction changed by 180o Then we follow the steps of vector addition 2.3 Adding and Subtracting Vectors Compare and contrast scalar and vector quantities.

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 @ 25o, and finally turns and goes 211 m @ -309o. What is his displacement?

2.4 Motion in Two Dimensions

SP1. Students will analyze the relationships between force, mass, gravity, and the motion of objects. f. Measure and calculate two-dimensional motion (projectile and circular) by using component vectors. Standard

2.4 Motion in Two Dimensions 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.

2.4 Motion in Two Dimensions 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.

2.4 Motion in Two Dimensions So if there is no gravity 2.4 Motion in Two Dimensions Measure and calculate two-dimensional motion by using component vectors.

2.4 Motion in Two Dimensions In the y axis, acceleration is always -9.80m/s2 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.

2.4 Motion in Two Dimensions 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.

2.5 Projectile Motion: Basic Equations We will assume no air resistance gravity is 9.80 m/s2 the Earth is not moving (Frame of Reference) That leaves the following variables X Y vx = voy = x = vy = t = a = -9.80 m/s2 y = 2.5 Projectile Motion: Basic Equations Measure and calculate two-dimensional motion by using component vectors.

2.5 Projectile Motion: Basic Equations The two axis are independent of each other except for time X Y vx = voy = x = vy = t = a = -9.80 m/s2 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 0o vx = vcosq = vcosq = v vy = vsinq = vsinq = 0 So our chart becomes X Y vx = v voy = 0 x = vy = t = a = -9.80 m/s2 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 = a = -9.80 m/s2 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 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 = a = -9.80 m/s2 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 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 = 1.3m/s voy = 0 x = vy = t = a = -9.80 m/s2 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 = 1.3m/s voy = 0 x = vy = t = a = -9.80 m/s2 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 = 1.3m/s voy = 0 x = vy = t = 0.505s a = -9.80 m/s2 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 = 1.3m/s voy = 0 x = vy = t = 0.505s a = -9.80 m/s2 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 = 1.3m/s voy = 0 x = vy = t = 0.505s a = -9.80 m/s2 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 = 1.3m/s voy = 0 x =0.656m vy = t = 0.505s a = -9.80 m/s2 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/s2 at an angle of 35o. 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 voy = x = vy = t = a = -9.80 m/s2 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 35o. What is displacement after 1.00s? X Y vx = voy = x = vy = t = 1.00s a = -9.80 m/s2 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 35o. What is displacement after 1.00s? vx = vcosq =20cos35 vx = 16.4m/s X Y vx = voy = x = vy = t = 1.00s a = -9.80 m/s2 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 35o. What is displacement after 1.00s? vx = vcosq =20cos35 vx = 16.4m/s X Y vx = 16.4m/s voy = x = vy = t = 1.00s a = -9.80 m/s2 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 35o. What is displacement after 1.00s? vy = vsinq = 20sin35 vx = 11.5 m/s X Y vx = 16.4m/s voy = x = vy = t = 1.00s a = -9.80 m/s2 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 35o. What is displacement after 1.00s? vy = vsinq = 20sin35 vx = 11.5 m/s X Y vx = 16.4m/s voy = 11.5m/s x = vy = t = 1.00s a = -9.80 m/s2 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 35o. What is displacement after 1.00s? x = vt x = (16.4)(1) = 16.4 X Y vx = 16.4m/s voy = 11.5m/s x = vy = t = 1.00s a = -9.80 m/s2 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 35o. What is displacement after 1.00s? x = vt x = (16.4)(1) = 16.4 X Y vx = 16.4m/s voy = 11.5m/s x = 16.4 m vy = t = 1.00s a = -9.80 m/s2 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 35o. What is displacement after 1.00s? y=voyt+½at2 y=11.5(1)+½(-9.8)(1)2 y=6.6m X Y vx = 16.4m/s voy = 11.5m/s x = 16.4 m vy = t = 1.00s a = -9.80 m/s2 y = 2.7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

displacement (magnitude) Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35o. What is displacement after 1.00s? displacement (magnitude) X Y vx = 16.4m/s voy = 11.5m/s x = 16.4 m vy = t = 1.00s a = -9.80 m/s2 y = 6.6m 2.7 General Launch Angle Measure and calculate two-dimensional motion by using component vectors.

displacement (magnitude) = 17.7 m direction Example: A projectile is launched with an initial speed of 20 m/s at an angle of 35o. What is displacement after 1.00s? displacement (magnitude) = 17.7 m direction X Y vx = 16.4m/s voy = 11.5m/s x = 16.4 m vy = t = 1.00s a = -9.80 m/s2 y = 6.6m 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 @ 22o, what is the maximum height that he reaches?

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 and grabs him. The bird is climbing with a velocity of 55 m/s @ 62o when he drops the gopher. If the gopher was 25 above the ground at the time, with what velocity does he strike the soft heather?

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

A-16 A dancing 2000 kg hippo leaps gracefully into the air. If she reaches a maximum height of 0.45 m and leaps at an angle of 35o. What was her initial velocity? What is her hang - time?

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

S-17 A killer tomato leaps at an unsuspecting dancing lady. If the tomato jumps with an initial velocity of 200 m/s @ 64o and lands on her 0.45 m above the ground, how far was he when he jumped?

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

S-18 A really cute bunny is tossed by his friends over a fence to a garden. If his initial velocity is 15 m/s @ 30o, and he starts from 5 m before the 2 m tall fence. Does he clear the fence? How much above or below the top of the fence does he go over (or hit)?

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

S-19 Dude is out jumping his windsurfer dude, when he catches a really cool wave dude. If the dude gets way up and like dude he reaches a height of 11.2 m. If he, dude, took off at an angle of 51o, dude..what was his original Velocity? Dude!

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

S-20 Three Giraffes named Ira, Samuel, and Lissette are singing a happy song when they are pushed off the cliff by an angry Badger. If they are pushed horizontally off a cliff that is 2000 m tall, with a speed of 114 m/s, how long do they have to keep singing their happy song. (any resemblance to real students is just a random coincidence)

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

S-21 A wolf named Sam is doing his best victory dance because his mom gave him a tasty package of dried squid. When an angry taco eating giraffe pushed him off a cliff. If the initial velocity of the wolf is 175 m/s @ 72o, what is the maximum height that the wolf reaches. (still no resemblance to any students)

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

S-22 Kermit “Baby Face” Frog shoots his AK-47 at an angle of 37o. The muzzle velocity of the gun is 700 m/s in the general direction of Miss Piggy. If the bullet lands at her feet, and Kermie shot the gun from 0.40 m in the air, how far away was Miss Piggy?

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

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