Trajectory: Simulate a Projectile Trajectory and Find Landing Position

Question

## Problem

Simulate the 2D trajectory of a projectile launched from the origin with initial speed V at angle theta (degrees from horizontal), subject to gravity g. Return the (x, y) coordinates sampled at each time step dt, and the landing position (where y first reaches 0 again).

```python
import math
from typing import List, Tuple

def simulate_trajectory(
    v: float,
    theta_deg: float,
    g: float = 9.81,
    dt: float = 0.01
) -> Tuple[List[Tuple[float,float]], Tuple[float,float]]:
    # returns: (list of (x,y) samples, (landing_x, landing_y))
    pass
```

**Example:**
```
trajectory, landing = simulate_trajectory(20.0, 45.0)
# landing -> approx (40.77, 0.0)
```

## Follow-ups

1. What angle maximizes range on flat ground, and does your simulation confirm it?
2. How would you add air resistance (drag proportional to velocity squared)? What changes in the update equations?
3. How would you determine if the projectile hits a target rectangle in its path?
4. How does reducing dt affect accuracy vs. runtime, and what is the trade-off called?

Trajectory: Simulate a Projectile Trajectory and Find Landing Position

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