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# Bellaire High School Advanced Physics - Chapter 3 - Projectile Motion

Bellaire High School Advanced Physics - Chapter 3 - Projectile Motion

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### Bellaire High School Advanced Physics - Chapter 3 - Projectile Motion

1. 1. Lesson 3-1 Review of Vectors
2. 2. Scalars and Vectors  Recall a scalar does not have a direction  A vector has BOTH magnitude and direction  Vectors can be added graphically 5 ¾¾® ¾¾® 8 9 ¾¾® ¬¾¾ 4 17 ¬¾¾ ¬¾¾ 5 5 ¬¾¾ ¬¾¾ 9 ¾¾® 14
3. 3. Similar Quantities  When adding vectors, the units must match  It would be meaningless to add a force vector to a velocity vector  They are essentially apples and oranges  When vectors do have the same units, we may add or subtract the vectors
4. 4. Example A student is walking to school. First, the student walks 350m to a friend’s house. The two then both walk 740 m to school. The method to add the vectors is called the tail to tip method. The vector we find is called the resultant vector.
5. 5. Moving Vectors  Vectors can be moved parallel to each other  Does not matter where the vectors are, as long as they are addable, tail to tip  Example  Push a toy car across a moving sidewalk  Say the sidewalk is moving at 1.5 m/s  The car is pushed .8 m/s
6. 6. Vector Addition and Subtraction  Vector addition is commutative  The order the vectors are added does not matter  To subtract a vector, simply add the opposite
7. 7. Multiplying and Dividing Vectors  Multiplying or Dividing vectors by scalars results in vectors  Lets say we have the velocity of a race car  We want to examine the properties of the car when it is traveling twice as fast  If vi is v, what is twice vi?  What is half of vi  What would be the new v if the car drove twice as fast in the opposite direction?
8. 8. Lesson 3-2 Vector Operations
9. 9. Coordinate Systems  Up to this point, we have only needed one dimension to study our situations  What if we wanted to study a ball being thrown at 45o above the ground?  That path of motion does not fit any of our current axis  We will have to use a combination of the two axis  Note: Orientation of the axis is up to you.
10. 10. Determining the Resultant  Trigonometry is very useful to find the resultant vector.  The Pythagorean Theorem  Think of a tourist in Egypt walking up the side of a pyramid  Are they walking vertical?  Are they walking horizontal?  It is a combination of the two motions that produces one final motion, somewhere between horizontal and vertical
11. 11. Resultant  The resultant of two vectors is also a vector  That means the resultant must have:  Magnitude  Direction  It is not enough to say the magnitude of the resultant, it must have direction also.  We will use the trig functions of sine, cosine or tangent to find the direction
12. 12. Resolving Vectors  Any vector may be broken into x and y components  That is to say any vector may be RESOLVED into its component vectors  A horizontal vector has a 0 y component  A vertical vector has a 0 x component  A vector at 45o has equal x and y vectors
13. 13. Examples  Page 92, Film Crew  Pg 93
14. 14. Non-perpendicular Vectors  Until now, all of our vectors have been perpendicular to each other  Things in real life are much, much less rigid  Lets say a plane travels 50 km at an angle of 35o, then levels out and climbs at 10o for 220 km  These vectors are not perpendicular, we cannot use the Pythagorean Theorem, yet  Resolve the vectors
15. 15. Lesson 3-3 Projectile Motion
16. 16. Two Dimensional Motion  In the last section, we resolved vectors into x and y components.  We will apply the same ideas to something thrown or flying in the air  Think of a long jumper  When she approaches her jump, she has only an x component  When she jumps, she has both x and y components
17. 17. Analyze Projectile Motion  We can break the motion into the two component vectors and apply the kinematic equations one dimension at a time  Any object thrown or launched into the air that is subject to gravity is said to have projectile motion  Examples?
18. 18. Projectile Path  Projectiles follow a path called a parabola  A common mistake is to assume projectiles fall straight down  Since there is vxi, there must be continuous horizontal motion Vx V Vy
19. 19. Projectile Path Vx V Vy  Neglecting air resistance, is there anything to stop the projectile in the horizontal direction?  Velocity in the horizontal direction is constant  In real life, horizontal velocity is not constant, but for our purposes we will assume uniform, constant velocity
20. 20. Projectile Path  Projectile motion is simply free fall with horizontal velocity  If two similar objects fall to the ground from the same height, one straight down while the other is thrown out to the side, which hits first?  It is very important to realize motion in the x direction is completely independent of motion in the y direction
21. 21. Summary  A projectile has horizontal velocity until the object stops (hits the ground)  A projectile will have a vertical velocity that is ever changing due to gravity, until the projectile stops (hits the ground)  What is the only factor that is consistent in the x AND y directions?  Time
22. 22. Projectile Path Vx V Vy Sample Pg 101, Practice Pg 102
23. 23. Objects Launched at an Angle  When an object is launched at an angle, the object has both horizontal and vertical velocity components  This is similar to the motion of an object thrown straight up with an initial vertical velocity  Example pg 103, Practice pg 104
24. 24. Lesson 3-4 Relative Motion
25. 25. Frames of Reference  Velocities are different in different frames of reference  You are in a train traveling at 40 km/h  Relative to the train, how fast are you moving?  Someone outside sees the train pass, how fast do they see you moving?  The velocities are different because the reference frames were different  You – Train, Outside observer - Earth
26. 26. Examples  You are driving on the interstate at 80 km/h and a car passes you at 90 km/h  How fast does it seem the passing car is moving to you? To someone on the side of the road?  A semi-truck driving west at 85 km/h passes a car on the other side of the road, driving east at 75 km/h. To the trucker, how fast is the car moving?
27. 27. Examples  A person standing on top of a train traveling at 20 km/h. They throw a baseball. How fast does it look like the ball is moving to a person standing on the ground when:  The ball is thrown 10 km/h forward  The ball is thrown 40 km/h backward  The ball is thrown 20 km/h backward  The ball is thrown straight up Example pg 108, Practice pg 109