Question

part c: use evidence from the reading to answer questions 1 and 2. 1. how do you calculate a bullet trajectory? give examples of reference points. 2. explain why a firearm crime is often complicated and trajectory difficult to determine.

Explanation:

Question 1: How do you calculate a bullet trajectory? Give examples of reference points.

Step 1: Identify Key Concepts

Bullet trajectory calculation involves physics (projectile motion) and forensic science. The basic projectile motion equations are used: $y = x\tan\theta - \frac{gx^2}{2v_0^2\cos^2\theta}$, where $x,y$ are coordinates, $\theta$ is the angle of fire, $v_0$ is initial velocity, and $g$ is gravity ($9.8\ m/s^2$).

Step 2: Reference Points

• Entry/Exit Wounds: On the victim/object, these give $(x,y)$ positions. For example, if a bullet enters a wall at $x = 5\ m$, $y = 1.5\ m$ (height) and exits at $x = 10\ m$, $y = 1.2\ m$, these points help determine the path.
• Firing Position: Estimated or known location of the shooter, providing an initial $(x_0,y_0)$. If the shooter is at $(0, 1.6\ m)$ (average height), this is a reference.
• Intermediate Obstacles: Bullet holes in furniture/walls between shooter and target, giving additional $(x,y)$ to refine the trajectory.

Step 3: Calculation Example

Suppose a bullet is fired with $v_0 = 300\ m/s$, $\theta = 5^\circ$, $x = 10\ m$.
First, calculate $\tan\theta \approx 0.0875$, $\cos\theta \approx 0.9962$.
Then, $y = 10(0.0875) - \frac{9.8(10)^2}{2(300)^2(0.9962)^2}$
$y \approx 0.875 - \frac{980}{2(90000)(0.9924)}$
$y \approx 0.875 - \frac{980}{178632} \approx 0.875 - 0.0055 \approx 0.8695\ m$.
This gives the height at $x = 10\ m$, helping map the trajectory.

1. Environmental Factors: Wind, air resistance (not accounted for in basic projectile equations), and uneven surfaces (e.g., a bullet ricocheting off a concrete floor) alter trajectory. For example, wind can deflect a bullet by several meters over long distances.
2. Multiple Shooters/Shots: In crimes with multiple firearms, distinguishing trajectories (different calibers, velocities) is hard. A crime scene with 3 shooters means 3+ trajectories to analyze.
3. Obstructions: Bullets pass through walls, furniture, or bodies, deforming and changing velocity/direction. A bullet hitting a door before the target will have its trajectory altered at the door’s impact point.
4. Lack of Reference Points: In chaotic scenes, entry/exit wounds or shooter positions may be unclear (e.g., a shooter fleeing, no known starting point). Without clear $(x,y)$ points, trajectory calculation is guesswork.
5. Human Error/Forensic Limitations: Forensic teams may misinterpret wounds (e.g., a grazing wound vs. a direct hit) or miscalculate initial velocity (if the firearm’s make/model is unknown, $v_0$ is estimated).

Answer:

Bullet trajectory is calculated using projectile motion equations (e.g., $y = x\tan\theta - \frac{gx^2}{2v_0^2\cos^2\theta}$) with reference points like:

• Entry/exit wounds (e.g., a bullet entering a wall at $(5\ m, 1.5\ m)$ and exiting at $(10\ m, 1.2\ m)$).
• The shooter’s position (e.g., $(0, 1.6\ m)$ as a starting point).
• Intermediate bullet holes (e.g., in a table at $(7\ m, 1.4\ m)$) to refine the path.

Question 2: Explain why a firearm crime is often complicated and trajectory difficult to determine.