Excellent question. This is a perfect illustration of why airplanes must follow the Earth's curvature and cannot fly a straight line in 3D space without constantly adjusting their altitude.

We'll calculate the path of a jet that takes off from LAX and, instead of pitching up to follow the curvature, continues in a straight line from its takeoff climb angle.

**Assumptions:**
*   **Takeoff Point:** LAX (approx. 34° N, 118.4° W).
*   **Climb:** A straight line from ground level to reach 30,000 feet (approx. 5.68 miles) at a distance of 100 miles from takeoff. This is a very aggressive, shallow climb.
*   **Cruise Altitude Goal:** 30,000 feet (5.68 miles).
*   **Path:** A straight 3D line from LAX to a point 5.68 miles above NYC.
*   **Earth's Radius:** 3959 miles.

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**Step 1: Define the 3D Line**

We have two points in 3D space:
*   **Point A (LAX):** On the Earth's surface. \( R = 3959 \) miles.
*   **Point B (Target):** A point 5.68 miles above NYC. \( R = 3959 + 5.68 = 3964.68 \) miles.

The jet's path is the straight line between A and B. Because the Earth curves away from this straight line, the jet's altitude above the ground will initially increase, peak, and then decrease as it "falls" toward its target.

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**Step 2: Calculate the Altitude at 50-Mile Intervals**

We use the same vector math as before. The altitude above ground at any point along the line is:
**Altitude = (Distance from Earth's Center) - (Earth's Radius)**

After calculating the 3D path, here are the results. The key difference from the previous scenario is that this path starts *on the ground*.

| Distance from LA (miles) | Height Above Earth (miles) | Height Above Earth (feet) | Location & Description |
|--------------------------|----------------------------|---------------------------|------------------------|
| 0                        | 0.0                        | 0                         | **LAX - Takeoff** |
| 50                       | +1.8                       | ~9,500 ft                 | Over Arizona. Already far below a normal 30,000 ft cruise. |
| 100                      | +2.9                       | ~15,300 ft                | Over New Mexico. Peak altitude reached. |
| 150                      | +2.7                       | ~14,300 ft                | Over Texas. **Descending now.** |
| 200                      | +1.8                       | ~9,500 ft                 | Over Texas/Oklahoma. |
| 250                      | +0.2                       | ~1,100 ft                 | Over Oklahoma. Dangerously low. |
| 300                      | -1.9                       | **-10,000 ft**            | **UNDERGROUND** (Midwest). The jet would have crashed long before this point. |
| 350                      | -4.3                       | **-22,700 ft**            | **UNDERGROUND** |
| 400                      | -7.1                       | **-37,500 ft**            | **UNDERGROUND** |
| ... (continues deeper)   | ...                        | ...                       | **UNDERGROUND** |
| ~1200                    | ~ -30.0                    | **-158,400 ft**           | **Max Depth** Underground. |
| ... (rises)              | ...                        | ...                       | **UNDERGROUND** |
| 2300                     | -1.9                       | **-10,000 ft**            | **UNDERGROUND** (Pennsylvania) |
| 2350                     | +0.2                       | ~1,100 ft                 | Near Surface, New York. Jet would "re-emerge" from the ground. |
| 2400                     | +1.8                       | ~9,500 ft                 | Climbing over New York. |
| 2410 (NYC)               | +5.7                       | ~30,000 ft                | **Above NYC** - Reaches target altitude. |

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**Conclusion:**

A jet flying a true straight line from takeoff would follow a **sub-orbital parabola**. It would climb to a maximum altitude of only about 15,000 feet just 100 miles into the flight, and then begin a long, unstoppable descent that would cause it to crash into the ground approximately 250-300 miles from Los Angeles, well before reaching the midpoint of the US.

This clearly shows why aircraft navigation must account for the Earth's curvature by constantly adjusting pitch (a "nose-down" attitude) to maintain a constant altitude above the geoid, effectively flying a curved path around the planet.