Do Now Someone throws a paper ball at

Do Now Someone throws a paper ball at you. You aren’t 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

BALLISTICS Trajectory motion

Trajectory What is it? Why do we care?

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.

Wind shield Distance along path of bullet to window, 23. 9” Path of bullet x y 60 feet Horizon Distance along horizon to window, 23. 5” Two reference points are needed to define the trajectory of the bullet So we know what to measure! Forensic Science: Fundamentals & Investigations, Chapter 17 Trajectory (this is a picture of the driver’s seat in a car. . ) 5

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. Forensic Science: Fundamentals & Investigations, Chapter 17 Trajectory 6

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

Wind shield Distance along path of bullet to window, 23. 9” Path of bullet x y 60 feet Horizon Distance along horizon to window, 23. 5” Given & Known Information: Building is 60 ft (720 inches away) Distance from window to bullet entrance is 23. 9 in. Horizontal distance from window to bullet entrance is 23. 5 in. Forensic Science: Fundamentals & Investigations, Chapter 17 Calculating Trajectory (Quick Similar Triangle Method) 8

QSTM What is distance from shooter to bullet entrance? Distance along path of (c) bullet to window, 23. 9” Distance along horizon to window, 23. 5” Building 720” away. What is the height of the shooter? (b)

QSTM: Ratios What is distance from shooter to bullet entrance? (c) Distance along path of bullet to window, 23. 9” Distance along horizon to window, 23. 5” Building 720” away. 23. 9” = c. 23. 5” 720”

QSTM What is distance from shooter to bullet entrance? (c) Distance along path of bullet to window, 23. 9” Distance along horizon to window, 23. 5” Building 720” away. 720” x 23. 9” = 23. 5” c

QSTM 732. 3” = c What is distance from shooter to bullet entrance? 732. 3” Distance along path of bullet to window, 23. 9” Distance along horizon to window, 23. 5” What is the height of the shooter? (b) Building 720” away.

Next step… What is the height of the shooter?

QSTM What is distance from shooter to bullet entrance? 732. 3” Distance along path of bullet to window, 23. 9” Distance along horizon to window, 23. 5” Pythagorean theorem! a 2 + b 2 = c 2 What is the height of the shooter? (b) Building 720” away.

QSTM • (732. 3”)2 = (720”)2 + b 2 • 536300 = 518400 + b 2 • 536300 – 518400 = b 2 • 17900 = b 2 • 133” = b What is distance from shooter to bullet entrance? 732. 3” Distance along path of bullet to window, 23. 9” Distance along horizon to window, What is the height of the shooter? (b) Building 720” away.

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

Worksheet Use the people around you!!

Exit Ticket The nearest building was 500 in away. The distance of the bullet from the window to the entrance on the seat was 10 in. 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?