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.

Crime Scene Reconstruction Trajectory Shooting distance Position and location of the victim Position and location of the offender Sequence of shots Direction of shots Possibility that the wound(s) could have been self inflicted Identification of weapon used may link serial cases

Important Forces  Forward force of the bullet  Downward force of gravity  To some extent:  Wind speed

 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.

8 Trajectory and Gravity  Bullet’s path is slightly curved  Gravity pulls it downward as the bullet moves forward Diagram is highly exaggerated

9 Determining the Location of the Shooter Building is 60 feet away along the horizon line Bullet hole is 4 feet above the ground Where is the shooter located?

Determining Location of Shooter  Need 2 reference points to make a straight line  Bullet holes in an object such as a wall, window or furniture  Bullet holes in a victim (entrance and exit count as two!)  Straight line tells investigators that shooter was somewhere on that line

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

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

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)

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”

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”

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”

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

Next step…  What is the height of the shooter?

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

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 = b – = b = b 2 133” = b

Just for fun….  What is the angle of impact?

How to read a right triangle  Sine, Cosine and Tangent are all based on a Right- Angled Triangle 22 "Opposite" is opposite to the angle θ "Adjacent" is adjacent (next to) to the angle θ "Hypotenuse" is the long one Adjacent is always next to the angle And Opposite is opposite the angle

Sine, Cosine and Tangent 23 Sine Function: sin( θ ) = Opposite / Hypotenuse Cosine Function: cos( θ ) = Adjacent / Hypotenuse Tangent Function: tan( θ ) = Opposite / Adjacent

Answer  Sin -1 (133/732.3) = ϴ = 10.5 ⁰  Cos -1 (720/732.3) = ϴ = 10.5 ⁰  Tan -1 (133/720) = ϴ = 10.5 ⁰

Exit Ticket  The nearest building was 500in away. The distance of the bullet from the window to the entrance on the seat was 20in. 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?  At a crime scene, police find a gunshot victim on a balcony 60 feet in the air. The bullet was shot from the ground and left the gun at an angle of 10 degrees from parallel. Determine how far away from the building the shooter’s location was.

Exit Ticket Answers  in; 441 in  340 ft