1. Equations of Motion

2. Equations of Motion Uniform Acceleration Uniform Motion d = vt
Pg. 27 #

3. Acceleration due to Gravity
Close to surface of a large body the acceleration due to gravity is constant
gEarth =
gMoon =
Air resistance depends on
Terminal Velocity is reached when
Pg. 37 #9, 12, 14

4. Ex. 1
What factors affect an object’s terminal speed? How does each factor affect the terminal speed?
Does the concept of terminal speed apply on the Moon? Why or why not?
The two main factors that affect terminal speed are mass and surface area. (For solid spherical objects, this is equivalent to saying that the terminal speed depends on the object’s density.) For objects of the same mass, an increased surface area contacting the air causes the terminal speed to become lower. For objects with the same surface area, the greater the mass the greater is the terminal speed.
There is no “terminal speed” related to air resistance on the Moon because the Moon does not have an atmosphere.

5. Ex. 2
Sketch a graph of the vertical speed as a function of time for a skydiver who jumps from an aircraft, reaches terminal speed, opens the parachute, and reaches a new terminal speed.
There are two terminal speeds in this case, a high
speed followed by a much lower terminal speed when
the parachute is opened. The graph is shown below.
The slope of the line near the beginning of the motion
is equal to the magnitude of the acceleration due to
gravity at that location. The terminal speed values are
found on page 39 of the text (Table 5).

6. Ex. 3
During the first minute of blastoff, a space shuttle has an average acceleration of 5g (i.e., five times the magnitude of the acceleration due to gravity on the surface of Earth). Calculate the shuttle’s speed in metres per second and kilometres per hour after 1.0 min. (These values are approximate.)

7. Ex. 4
A flowerpot is dropped from the balcony of an apartment, 28.5 m above the ground. At a time of 1.00 s after the pot is dropped, a ball is thrown vertically downward from the balcony one storey below, 26.0 m above the ground. The initial velocity of the ball is 12.0 m/s [down]. Does the ball pass the flowerpot before striking the ground? If so, how far above the ground are the two objects when the ball passes the flowerpot?

8. Work on Graph Worksheet
Graphical Analysis
Work on Graph Worksheet
*** Use Logger Lite Experiment (35e Graphing Your Motion)

9. 1. Using the graph, determine each of the following.
(ans: m/s)
(ans: B:1.1m/s)
(t = 8.2 s, 12.5 s, 14.5 s)
(a) the average velocity for the first 2.5 s
(b) the instantaneous velocity at the points B.
(c) the times at which the instantaneous velocity is approximately zero.

10. 2. A ball rolls along the floor, up a sloping board, and then back down the board and across the floor again. The graph below represents this motion.
(a) At what time is the ball at its highest point?
(b) What was the acceleration when the ball was (i) rolling up the board, (ii) rolling down the board, and (iii) at rest at the top point?
(c) How far up the board did the ball go?
(d) What was the total displacement of the ball over the 9.0 s trip?
(ans: 4.5 s)
(ans: m/s2)
(ans: 1.2 m)
(ans: 0 m)
(e) Draw the corresponding position-time graph.

11. Vectors in 2-D

12. Vector Components : In General
For any vector with magnitude |v|
Define θ at its base to the horizontal
|v| θ

13. Vector Components (cont.)
Any vector can be written as the sum of perpendicular unit vectors
Standard Form: Magnitude [ N of W]
Component Form: (Magnitude x + Magnitude y) Units
Ex. Write in component form: 30 km [30 E of N]
Ex. Write in vector form: (3x - 4y) cm/s
Ex. Pg. 29 #
Ex.

14. Adding Vectors
We add vectors using the tip-to-tail method

15. Adding Vectors (Cont.) Given two vectors that we are adding
What is their resultant
i.e. v1 + v2 = v3
What is the magnitude
and direction of v3 ?
Add up all the horizontal components
Add up all the vertical components
Then use Pyth. Theorem and trig to find Magnitude of v3 and direction (ө) ө

16. Ex. 1
While out shopping in New York, Melissa got lost. Tracing back her steps, she had walked 100 m [SE], and 600 m [W20°S]. The whole trip took 1.3 hours.
Determine the distance traveled and resultant displacement.
Determine her average speed and velocity.

17. Ex. 2
A ball rolling with an initial velocity of 30 m/s [W] undergoes an acceleration of 8.0 m/s2[N] for a period of 8.0 seconds. (a) What is the final velocity of the ball? (b) What is the displacement of the ball in the 8.0 s?

18. Ex. 3
Jim is 200 m[S] of Mary. Mary begins to walk East at 3.00 m/s the same time that Jim begins to walk West at 4.00 m/s. What is the displacement of Jim from Mary 50.0 seconds later?

19. SPH4U – RELATIVE VELOCITY

20. For each of the following, perform the vector operation indicated to find either the sum or the difference vector.

21. Relative Velocities Frames of Reference
A frame of reference is a coordinate systems in which motion can be described
All velocities are measured relative to a frame of reference
Different frames of reference will describe motion in different ways
We can easily move between frames that are moving at constant velocities

22. Moving between frames In Air: In Water:
vPG = velocity of plane w/ wind
vSG = velocity of swimmer w/ current
vPA = velocity of plane w/ no wind
vSW = velocity of swimmer w/ no current
vAG = velocity of wind
vWG = velocity of current

23. Ex. 2: (pg 56 # 4)
A plane, travelling with a velocity relative to the air of 320 km/h [28° S of W], passes over Winnipeg. The wind velocity is 72 km/h from the North. Determine the displacement of the plane from Winnipeg 2.0 h later.
7.2 x 102 km [38º S of W] from Winnipeg

24. Projectile Motion

25. Projectile Motion
A projectile is an object that only moves under the influence of gravity
A trajectory is the path a projectile takes through the air
The vertical and horizontal components of motion are independent
Pg. 46 #3, 4
Pg. 50 #10
Ex. Monkey Gun!

26. Symmetric Trajectories
Ex. What angle should you fire for maximum time of flight?
Ex. What angle should you fire for maximum range?
Ex. What angle should you fire for maximum height?
Ex. Can two firing angles result in the same horizontal range? Why?

27. Analysis of Projectile Motion
Horizontal (x)
Vertical (y)
- Uniform Motion (ignoring air resistance)
- v1x = v1cosӨ
- v2x = v1x
- ∆t is the same in both components
- dx = v1x ∆t
- Uniform acceleration
- Acceleration due to gravity, ay = g
- v1y = v1sinӨ
- ∆dy = change in height
(up = +ve, down = -ve)
- Use kinematics equations to find ∆t and v2y

28. Ex 1:
A marble rolls off a table with a velocity of 1.93 m/s [horizontally]. The tabletop is 76.5 cm above the floor. If air resistance is negligible, determine
(a) how long the marble is airborne
(b) the horizontal range
(c) the velocity at impact

29. Ex 2:
A seagull with a rocket strapped on its back is diving towards its target at an angle of 45o below the horizontal and at a speed of 320 m/s. When the seagull is 600 m above the ground, it releases its load, which then hits the target.
How long before the “bomb” hits its target?
What horizontal distance will the “bomb” travel?
What final velocity does the “bomb” hit the target?

30. Projectile Motion (2 objects)

31. During the 2013 World Series between the Cardinals and the Red Sox, a ball was batted from home plate, 1.00 m above ground, at v1 km/h, θ degrees above the horizontal. An outfielder, standing 70.0m from home plate, accelerated from rest at 3.60m/s2 for 3.00s to catch the ball when it returned to its initial height. Determine the initial velocity of the ball.