1. Someone throws a paper ball at you. You arent looking their direction when it was thrown, but you turn around right before it hits you in the forehead. Can you usually tell where it came from? Can you tell who threw it? How? (((NO need to demonstrate this ))) Do Now

2. BALLISTICS Trajectory motion

3. Trajectory What is it? Why do we care?

4. Ballistics Bullet Trajectory and Path Since bullets obey the laws of physics it is easy to determine their origin and distance traveled. This can be done by using dowels, lasers, or our brains.

5. Two reference points are needed to define the trajectory of the bullet So we know what to measure! Path of bullet Horizon Wind shield Distance along path of bullet to window, 23.9 Distance along horizon to window, 23.5 y x 60 feet

6. Reference points can be bullet holes in objects or victims. An entry point and exit point on a victim can be used. Gunshot residue or spent cartridge casings can be less specific reference points. Investigators can use lasers to trace a straight-line path to help determine the position of the shooter.

7. Triangle Basics!!! If two triangles are SIMILAR, what does that mean? If two triangles are SIMILAR, what does that mean? What does that mean about their ratios? What does that mean about their ratios? What does that mean about calculating side lengths? What does that mean about calculating side lengths?

8. Given & Known Information: Building is 60ft (720 inches away) Distance from window to bullet entrance is 23.9in. Horizontal distance from window to bullet entrance is 23.5in. Path of bullet Horizon Wind shield Distance along path of bullet to window, 23.9 Distance along horizon to window, 23.5 y x 60 feet

9. Distance along path of bullet to window, 23.9 Distance along horizon to window, 23.5 Building 720 away. What is distance from shooter to bullet entrance? (c) What is the height of the shooter? (b)

10. Distance along path of bullet to window, 23.9 Distance along horizon to window, 23.5 Building 720 away. What is distance from shooter to bullet entrance? (c) 23.9 = c. 23.5 720

11. Distance along path of bullet to window, 23.9 Distance along horizon to window, 23.5 Building 720 away. What is distance from shooter to bullet entrance? (c) 23.9 = c. 23.5 720

12. Distance along path of bullet to window, 23.9 Distance along horizon to window, 23.5 Building 720 away. What is distance from shooter to bullet entrance? (c) 720 x 23.9 = c 23.5

13. Distance along path of bullet to window, 23.9 Distance along horizon to window, 23.5 Building 720 away. What is distance from shooter to bullet entrance? 732.3 What is the height of the shooter? (b) 732.3 = c

14. Next step… What is the height of the shooter?

15. Distance along path of bullet to window, 23.9 Distance along horizon to window, 23.5 Building 720 away. What is distance from shooter to bullet entrance? 732.3 What is the height of the shooter? (b) Pythagorean theorem! a 2 + b 2 = c 2

16. Distance along path of bullet to window, 23.9 Distance along horizon to window, 23.5 Building 720 away. What is distance from shooter to bullet entrance? 732.3 What is the height of the shooter? (b) (732.3) 2 = (720) 2 + b 2 536300 = 518400 + b 2 536300 – 518400 = b 2 17900 = b 2 133 = b

17. 1. The nearest building was 500in away. The distance of the bullet from the window to the entrance on the seat was 10in. The horizontal distance from the entrance to the window is 7. What is the distance of the shooter to the bullet entrance and how high up was the shooter? 2. Do the practice problems on the trajectory worksheet. 3. Be sure to put all given information & show your work (SHOW YOUR TRIANGLES). 4. CHALLENGE!!!!!: Try to complete 9 and 10 without help. If time, we will discuss.

18. Worksheet Use the people around you!!

19. Exit Ticket The nearest building was 500in away. The distance of the bullet from the window to the entrance on the seat was 10in. The horizontal distance from the entrance to the window is 15. What is the distance of the shooter to the bullet entrance and how high up was the shooter?