Physics and Honors Physics – Kinematics



I. Vectors: The Basics

• Recall the difference between a scaler and a vector

scaler vector

magnitude only magnitude and direction

ex. Distance ex. Displacement

speed velocity

time acceleration

mass force

temperature

We will graphically represent vectors using arrows. The length of the arrow represents the (relative) magnitude and the arrow will point in the direction of the vector.

Ex: v1 = 20m/s North Ex: v2= 40 m/s West

V2 is drawn approximately twice as long as v1 because 40m/s is twice as fast as 20m/s

Vector Addition:

When combing (“adding”) vectors. You must pay attention to the direction. You don’t always just “add” them.

EX. You travel 10km north then an additional 15 m north. What’s your displacement?

* So yes in this case you “added”

Ex You travel 10 km north and then 15m south. What is your displacement?

* in this case you “added” a negative

Ex. You travel 10km north then 15 km east. What is your displacement?

*because you are working in 2-D, you cant just simply add algebraically.

Pythagorean theorem will give you the magnitude

What about direction? To get direction plot x first and then y distance. PLOT HEAD TO TAIL. This will always allow for “regular” directions.

* calculator plug in = inverse tan (10/15)

it will look like tan-1 (10/15) in your calculator

Degree and Direction: explanation

* if no direction is given (ex.Travel 10m NE)then take degree angle to be 45°

Ex.

II. Vector Resolution

- to resolve a vector means to break it apart into its x and y components

Ex. A car drives 40m at 60° NW. How far north and west did it travel?

Day 2 Vectors:

*things you already know:

Two vectors that are perpendicular to each one = use Pythagorean Theorem

How do you combine vectors that are NOT at right angles (perpendicular) to each other?

THE COMPNENT METHOD OF VECTOR ADDITION

TAKE YOUR TIME! One mistake has a snowball effect

A method for “adding” vectors that are not perpendicular to one another

1. VISULAIZE Situation – DRAW A PICTURE

2. RESOLVE each vector into its x and y components. Pay attention to the direction of the componenets (north and east are positive…..south and west are negative)

3. Find the NET x and y vectors

4. PLOT the net x and y vectors (Head to tail method)

5. Use TRIG to find the resultant vector magnitude and direction

Looking for an immunity idol a survivor runs 33m 40° NE, then 20m South and finally 20°SE. What is her overall displacement?

Now you try: An ostrich walks 35m NW and then goes 40m 15° WS and then finally 2m W. What is his final displacement?

Ans: 39.61m 20.5° SW

Day 3 Vectors - using vectors to solve relative motion problems (ie: train problems)

*How do you know an object is moving?

ALL MOTION IS RELATIVE (that is all objects move with relation to (w/r/t) other objects.

( in order to describe the motion of an object it must be compared to another object.

- compare its motion to something “stationary”

(usually this is the background)

Mathematically ……….

If objects moving in opposite directions = ADD the vectors to fins relative motion

Velocity A Velocity B = ADD

If objects moving in same direction = SUBTRACT to find relative motion

Velocity A Velocity B = SUBTRACT

EX.

D’Angelo drives the pick-up truck. What is D’Angelo’s speed with respect to the following?

The mini van? The green car?

The road? His car?

EX 2. Suppose the pick-up truck is initially 0.25 miles behind the mini van. Assume all automobiles are traveling at constant speeds.

a. can the pick up truck catch up to the mini van?

b. What time would it take to catch up to the mini van?

c. What distance did the pick up truck travel in order to reach the mini van.

DEMO: Launch

a. Which ball travels the greater distance?

b. Which ball travels faster?

c. Which ball hits the ground first?

• ALL bodies fall at the same rate of (VERTICAL) acceleration regardless of the horizontal motion!!!!

• Gravity is a force that pulls you vertically*, therefore the acceleration due to this force is always vertical (no matter if there is horizontal motion).

• The only common factor between the horizontal and vertical motion is TIME!!!!!

IV. Projectile Motion – a combination of vertical and horizontal motion video(stop at 2:20)

The vertical motion is independent of the horizontal motion.

• The only common factor between the horizontal and vertical motion is TIME!!!!!

• Demo: Launcher Cart (where should the ball land?) Water and projectile motion

EX. Miss Boron likes to play practical jokes. She goes to the school roof (12.0m off the ground) with water balloons and launches the balloon. If Miss Boron throws the balloon with an initial horizontal speed of 7.9m/s, will she hit the student? The student is 13.0m away from the edge of the building.

a. Question is looking for the range of the balloon?

b. What is the final velocity right before the balloon hits the ground?

|VARIABLE |X |Y (UP) |Y (DOWN) |

|Vo | | | |

|Vf | | | |

|a | | | |

|d | | | |

|t | | | |

Day 2 Projectiles-

EX. A child kicks a ball 13m/s at an angle of 30° above the ground.

a. Max height of the ball

b. Time of the flight

c. Range of the ball

d. What other angle could the child have kicked the ball to produce the same range?

|VARIABLE |X |Y (UP) |Y (DOWN) |

|Vo | | | |

|Vf | | | |

|a | | | |

|d | | | |

|t | | | |

d.Remember this video from yesterday?

Neglecting Air resistance, complementary angles will give the same horizontal range.

Therefore a _______ angle will produce the same range.

Solve problem for the complimentary angle and see if you get same range. TRY IT (

Day three projectiles -

EX. Mrs McGrath liked Miss Boron’s joke so much she headed to the edge of the media center with a water balloon! Mrs McGrath spots a student and thorws. She hits the student 8.0m away from the edge of the building. Assuming she threw the balloon with a horizontal speed of 5.9m/s, how high is the edge of the media center roof?

OMG is she trying to drive us crazy……this stuff is hard……will there be extra credit

|VARIABLE |X |Y (UP) |Y (DOWN) |

|Vo | | | |

|Vf | | | |

|a | | | |

|d | | | |

|t | | | |

Theory Review:

Shoot the monkey thought question Answer: shoot the monkey

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sin Ÿ[pic] = opp

Hyp

cos Ÿ[pic] = adj

Hyp

tan Ÿ[pic] = opp

adj

N

S

E

W

30°

10°

10°

25° NE

75° NW

60° SE

70° SW

N

S

E

W

Ÿ[pic]

[pic]

55 mph

45 mph

35 mph

[pic]

Neglecting Air resistance let’s consider the following…

Imagine rolling a ball (at a uniform speed) across the table…

…IF there was no gravity it would continue to move horizontally (at the same level) WITH THE SAME speed.

The horizontal motion is uniform (no acceleration) so we can use

v = d/t

Imagine dropping a ball from the edge of a table…

…dropped from rest, it will accelerate as it falls.

GRAVITY governs the vertical motion (use the big five and a = ±9.8 m/s2)

Vf2 = Vo2 + 2ad

d = vot + ½ at2

a = (vf – vo)/t

Projectile Motion

Projectile Motion is the curved motion of an object launched through the air.

It is the combination of uniform horizontal motion and accelerated vertical motion

Trajectory – the path of a projectile

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