Kinematics

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

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

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

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. = 0 Projectile Motion Assumptions At the maximum height:

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

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-2You 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: 281.91 ft

37. Projectile MotionThe Ballistic Device

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

39. Projectile MotionThe 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 MotionThe Ballistic Device Final Test: Land in a target specified by the teacher on day of test

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

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

45. Projectile MotionThe Ballistic Device Finding Formula for Initial Velocity:

46. Projectile MotionThe Ballistic Device Finding Formula for Initial Velocity:

47. Projectile MotionThe Ballistic Device Finding Formula for Initial Velocity:

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

49. Projectile MotionThe Ballistic Device Finding Formula for Initial Velocity:

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