1. Unit 8 POE Ballistic Device
Kinematics
Unit 8
POE Ballistic Device

2. What is Kinematics?
Kinematics is the study of the geometry of motion and is used to relate displacement, velocity, acceleration and time without reference to the cause of motion.

3. The Language of Kinematics
Distance
Displacement
Velocity
Speed
Acceleration

4. The Language of Kinematics
Scalar Quantities:
Quantities that are fully described by magnitude alone
ex: Temperature = 14 degrees F
Energy =1500 calories
Time = 30 seconds

5. The Language of Kinematics
Vector Quantities:
Quantities that are fully described by BOTH a magnitude and a direction
ex: Distance = 1 mile, Northeast
Velocity = 75 mph, South
Force = 50 pounds, to the right (East)

6. The Language of Kinematics
Distance (d): Scalar Quantity
How far an object has traveled during its time in motion.
Ex: A person walking ½ mile to the end of the trail and then returning on the same route, the distance walked is 1 mile. d = 1 mile

7. The Language of Kinematics
Displacement (s): Vector Quantity
A measure of an object’s position measured from it’s original position or a reference point.
The terms displacement and distance are used interchangeably, although not always correctly

8. The Language of Kinematics
Distance: length traveled along a path
between 2 points
Start
End
Displacement: straight line distance
between 2 points
Start
End

9. The Language of Kinematics
Displacement can be measured as two components, the x and y direction:
Start
End
X displacement
Y displacement

10. The Language of Kinematics
Speed: Scalar Quantity
The rate an object is moving without regard to direction.
The ratio of the total distance traveled divided by the time
Ex: A car traveled 400 miles for 8 hours. What was its average speed? Speed= 50 mph

11. The Language of Kinematics
Velocity (v): Vector Quantity
The rate that an object is changing position with respect to time
Average Velocity is the ratio of the displacement divided by the time.
The terms velocity and speed are sometimes used interchangeably, although not always correctly.

12. The Language of Kinematics
Velocity (v): Vector Quantity
Ex: What would be the average velocity for a car that traveled 3 miles north in a total of 5 minutes?

13. The Language of Kinematics
Acceleration (a): Vector Quantity
The rate at which an object is changing its velocity with respect to time
Average Acceleration is the ratio of change in velocity divided by the elapsed time (change in time)

14. The Language of Kinematics
Acceleration (a): Vector Quantity
Ex: Assume that a car, who starts at rest, is going 50 m/s (meters per second) after 5 seconds. What is it’s average acceleration?

15. Projectile Motion – Motion in a plane
Motion in 2 directions: Horizontal and Vertical
Horizontal motion is INDEPENDENT of vertical motion
Path is always parabolic in shape and is called a Trajectory
Graph of the Trajectory starts at the origin.

16. Projectile Motion Assumptions
Curvature of the earth is negligible and can be ignored, as if the earth were flat over the horizontal range of the projectile
Effects of wind resistance on the object are negligible and can be ignored

17. Projectile Motion Assumptions
The variations of gravity (g) with respect to differing altitudes is negligible and can be ignored.
Gravity is constant: or

18. Projectile Motion Assumptions
To start:
Horizontal Direction, x, represents the range, or distance the projectile travels
Vertical Direction, y, represents the altitude, or height, the projectile reaches

19. Projectile Motion Assumptions
Horizontal Direction:
No acceleration therefore ax = 0
Vertical Direction:
Gravity affects the acceleration. It is constant and directed downward, therefore ay = -g.

20. Projectile Motion Assumptions
At the maximum height:
= 0

21. Projectile Motion Formulas
Horizontal Motion:
The x position is defined as:

22. Projectile Motion Formulas
Horizontal Motion:
Since the horizontal motion has constant velocity and the acceleration in the x direction equals 0 (ax = 0 because we neglected air resistance) , the equation simplifies to:

23. Projectile Motion Formulas
Vertical Motion:
The y position is defined as:

24. Projectile Motion Formulas
Vertical Motion:
Since vertical motion is accelerated due to gravity, ay = -g, the equation simplifies to:

25. Projectile Motion Formulas
Going one step further:
There is a right triangle relationship between the velocity vectors – Use Right Triangle Trigonometry to solve for each of them!

26. Projectile Motion Formulas

27. Projectile Motion Formulas

28. Projectile Motion Formulas
Horizontal Motion:
Combine the two equations:
and

29. Projectile Motion Formulas
Vertical Motion:
Combine the two equations:
and

30. Projectile Motion Problem
A ball is fired from a device, at a rate of 160 ft/sec, with an angle of 53 degrees to the ground, it lands after 8 seconds.

31. Projectile Motion Problem
Find the x and y components of Vi.
What is the ball’s range (the distance traveled horizontally)?

32. Projectile Motion Problem
Find the x and y components of Vi.
Vi = initial velocity = 160 ft/sec

33. Projectile Motion Problem
Find the x and y components of Vi.

34. Projectile Motion Problem
What is the ball’s range (the distance traveled horizontally)?

35. Projectile Motion Problem-2 You try one:
A golf ball is hit at an angle of 20 degrees from the ground, with an initial velocity of 100ft/sec. It lands on the ground after 3 seconds.

36. Answers:
Horizontal Distance: ft

37. Projectile Motion The Ballistic Device

38. Projectile Motion The Ballistic Device
Objective:
Create a device that will toss a projectile (ping-pong ball) accurately within a given range

39. Projectile Motion The Ballistic Device
Constraints:
Range between 5 and 15 feet
Fit inside a 1 ft x 1 ft footing
No high-power pressure gasses or combustibles
Constructed from found materials

40. Projectile Motion The Ballistic Device
Final Test:
Land in a target specified by the teacher on day of test

41. Projectile Motion The Ballistic Device
Method:
Calculate initial Velocity (Vi), and assume it stays constant throughout the test
Calculate resulting range for specified angles
Plot range vs angle and use to predict angle for specified range

42. Projectile Motion The Ballistic Device
Calculate Initial Velocity:
Pick an angle
Shoot projectile 10 times at chosen angle and calculate the mean range
Use the angle, mean range and gravity constant to calculate initial velocity

43. Projectile Motion The Ballistic Device
Finding Formula for Initial Velocity :
Remember?
and
Both involve time (t) which is extremely difficult to measure accurately

44. Projectile Motion The Ballistic Device
Finding Formula for Initial Velocity :
For entire motion, total vertical displacement = 0, therefore y = 0.

45. Projectile Motion The Ballistic Device
Finding Formula for Initial Velocity:

46. Projectile Motion The Ballistic Device
Finding Formula for Initial Velocity:

47. Projectile Motion The Ballistic Device
Finding Formula for Initial Velocity:

48. Projectile Motion The Ballistic Device
Finding Formula for Initial Velocity:
Trigonometric Identity:

49. Projectile Motion The Ballistic Device
Finding Formula for Initial Velocity:

50. Projectile Motion The Ballistic Device
Finding Formula for Range knowing Initial Velocity and Angle:

51. Projectile Motion The Ballistic Device
Finding Formula for Range knowing Initial Velocity and Angle:

52. Projectile Motion The Ballistic Device
Finding Formula for Range knowing Initial Velocity and Angle:
Using this formula, the range (x) can be calculated for various angles