1. Unit 4 Vectors & 2-D/Parabolic Motion

2. Physics Comp Book UNIT 4: Vectors & 2-D/Projectile Motion
Student will:
SP1b. compare and contrast scalar and vector quantities;
SP1c. compare algebraically the relationships between time, distance, velocity and acceleration;
SP1f. measure and calculate two dimensional motion (projectile…) by using component vectors
Page Contents
22 parabolic motion, projectile
23 range, time of flight
24 trajectory, Pythagorean theorem
25 vectors, triangles and trigonometry diagrams
26 Ex: solving a 2-D problem
27 Lab SUMUP:

3. One dimension vs. two dimensions
So far, we have only talked about the motion of objects that travel in either the x or the y direction… only one dimension at a time.
What do these vectors look like:
a ball thrown directly up?
a car traveling on a highway?

4. One dimension vs. two dimensions
…but sometimes, things don’t travel in a direction that’s completely vertical or completely horizontal…for example, what would these vectors look like:
A football field goal kick?
A basketball free throw shot?
How about a ballerina leaping across the stage?
A ball rolled off the edge of a table?
Notice how the initial velocity is a certain direction and the motion path doesn’t continue in that same direction…look at the next examples, too…

5. In the absence of gravity a bullet
would follow a straight line forever.
With gravity it FALLS AWAY from
that straight line!

6. Football without gravity and with…

7. Basketball – with and without gravity

8. Hitting the target – aim high, not directly at the target
BULLSEYE!

9. Projectile Examples These are all examples of things that are
projected, then go off under the
influence of gravity
Hockey puck
Basketball
Volleyball
Arrow
Shot put
Javelin
Tennis ball
Golf ball
Football
Softball
Soccer ball
Bullet

10. Not projectiles Jet plane Rocket
Car (unless it looses contact with ground)
Why are these things NOT projectiles?

11. Path of the Projectile g falling rising Height v Distance downfield
(range)
Horizontal velocity
Vertical
velocity v
projectile

12.  The key to understanding
projectile motion is to realize
that gravity acts vertically
 it affects only the vertical
part of the motion, not the
horizontal part of the motion

13. Vectors first, then the path…
In order to describe the motion of objects like this, we have to learn about the initial vectors FIRST.
After that we will learn how to calculate:
How high…
How far …
How long …
How fast…

14. Vectors at an angle…
A vector in 2-D is made of an x-component and a y-component.
Finding the components of a 2-D vector is called RESOLVING the vector
To find the values of these components, we use trigonometry.
Vector
y component
X component

15. Trigonometry Overview
SOH CAH TOA
Hypotenuse
Vector
opposite
y component 
X component
adjacent

16. Example: Resolving a Vector
Write this example in your comp book p. 25
A football is kicked with an initial velocity of 15 m/s at 30º above the horizon. What are the x- and y-components?
Resolving a vector:
Label parts of triangle.
Choose a trig function for the missing information.
Use your calculator. 
Vx = 15 cos 30 = 13 m/s
Vy = 15 sin 30 = 7.5 m/s

17. Using components to make a 2-D vector
A vector in 2-D is made of an x-component and a y-component.
When the vectors occur in ONE dimension, you can just add/subtract.
But when you combine vectors in 2-D, you have to use trig…
Vector
y component
X component

18. Using components to make a 2-D vector
Let the x- and y-components be the sides of a right triangle.
Draw a diagonal line. This is the hypotenuse of the right triangle AND…
It’s the RESULTANT vector.
Use Pythagorean theorem to determine the MAGNITUDE:
a2+ b2 = c2
Use tangent to determine the DIRECTION (the angle).
Vector
y component
X component

19. Example: Finding the resultant vector
Write this example in your comp book p. 25
You walk 6 blocks east and then 13 blocks north. What is your displacement from home?
Hint: solve for magnitude then direction…
13 blks
6 blks
Home

20. Example - Answer
Home
6 blks
13 blks

21. Example - Answer #1
Home
6 blks
13 blks
14.32 blks 

22. Demonstration
We can see that the horizontal and vertical motions are independent
The red ball falls vertically
The yellow ball was given a kick to the right.
They track each other vertically step for step and hit the ground at the same time

23. Projectile motion – key points
The projectile has both a vertical and horizontal component of velocity
The only force acting on the projectile once it is shot is gravity (neglecting air resistance)
At all times the acceleration of the projectile is g = m/s2 (downward)
The horizontal velocity of the projectile does not change throughout the path

24. Key points, continued
On the rising portion of the path, gravity causes the vertical component of velocity to get smaller and smaller
At the very top of the path, the vertical component of velocity is ZERO
On the falling portion of the path, the vertical velocity increases

26. More key points
If the projectile lands at the same elevation as its starting point, it will have the same final vertical SPEED as initial (opposite velocity)
The time it takes to get to the top of its path is the same as the time to get from the top back to the ground.
The range of the projectile (where it lands) depends on its initial speed and angle of elevation

27. Example:
A 2.00 m tall basketball player wants to make a basket from
a distance of 10.0 m. If he shoots the ball at a 450 angle, at
what initial speed must he throw the ball so that it goes
through the hoop without striking the backboard? y x y0

28. Maximum Range
When an artillery shell is fired the initial speed of the projectile depends on the explosive charge – this cannot be changed
The only control you have is over the angle of elevation.
You can control the range (where it lands) by changing the angle of elevation
To get maximum range set the angle to 45°

29. Interactive

30. The ultimate projectile: Putting an object into orbit
Imagine trying to throw a rock around the world.
If you give it a large
horizontal velocity,
it will go into orbit
around the earth!