he Enterprise is travelling at 0.80c when it fires a missile at 0.95c relative to itself. How fast
would the missile approach an asteroid as measured by a stationary probe?

To find the velocity of the missile relative to a stationary probe, we need to use the **relativistic velocity addition formula** because the velocities involved are a significant fraction of the speed of light \(c\).

The relativistic velocity addition formula is:

\[
v = \frac{v_1 + v_2}{1 + \frac{v_1 v_2}{c^2}}
\]

Where:
- \(v\) is the velocity of the missile relative to the stationary probe.
- \(v_1 = 0.80c\) is the velocity of the Enterprise relative to the stationary probe.
- \(v_2 = 0.95c\) is the velocity of the missile relative to the Enterprise.
- \(c\) is the speed of light.

### Step-by-step calculation:

\[
v = \frac{0.80c + 0.95c}{1 + \frac{(0.80c)(0.95c)}{c^2}}
\]

Simplifying:

\[
v = \frac{1.75c}{1 + \frac{0.80 \times 0.95}{1}}
\]
\[
v = \frac{1.75c}{1 + 0.76}
\]
\[
v = \frac{1.75c}{1.76}
\]

Now, calculating the result:

\[
v \approx 0.994c
\]

### Conclusion:
The velocity of the missile relative to the stationary probe is approximately \(0.994c\).

Would you like more details or have any further questions?

Here are five related questions to consider:
1. What happens to velocities as they approach the speed of light according to special relativity?
2. How does the relativistic velocity addition formula differ from classical velocity addition?
3. Why can't objects with mass reach the speed of light?
4. What are some other effects of special relativity at high speeds (e.g., time dilation)?
5. How would time appear to pass for an observer on the missile compared to the stationary probe?

**Tip**: Relativistic effects become significant when velocities are a large fraction of the speed of light, making classical mechanics less accurate.

The Enterprise is travelling at 0.80c when it fires a missile at 0.95c relative to itself. How fast would the missile approach an asteroid as measured by a stationary probe?

This solution explains how to calculate the speed of a missile fired from the Enterprise (moving at 0.80c) as it approaches an asteroid, using the relativistic velocity addition formula. Suitable for undergraduate physics students studying special relativity.

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