Post on 31-Mar-2015
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 )))
Do Now
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.
Trajectory (this is a picture of the driver’s seat in a car..)
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Two reference points are needed to define the trajectory of the bulletSo 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”
yx
60 feet
Trajectory
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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.
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?
Calculating Trajectory (Quick Similar Triangle Method)
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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”
yx
60 feet
QSTM
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)
QSTM: Ratios
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”
QSTM: Ratios
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”
QSTM
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”
QSTM
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?
QSTM
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! a2 + b2 = c2
QSTM
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 + b2
• 536300 = 518400 + b2
• 536300 – 518400 = b2
• 17900 = b2
• 133” = b
Practice QSTM Trajectory
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.
Worksheet
Use the people around you!!
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?