Observer Sees When I Throw Ball at Speed of Light

[jirakst]

If I were of speed 299 792 457 m/s relative to an observer and throw a ball, what would the observer see?

 

[beamie564]

The observer would see the ball go very fast, with velocity $v= \frac{u+w}{1+\frac{uw}{c^2}}$ where $u$ and $w$ are yours and the ball's speed respectively.

 

[Nugatory]

The observer would see the ball go very fast, with velocity $v= \frac{u+w}{1+\frac{uw}{c^2}}$ where $u$ and $w$ are yours and the ball's speed respectively.

...where $u$ is your speed relative to the observer and $w$ is the speed at which you throw the ball relative to you.
You can simplify the formula a bit by choosing to measure time in seconds and distances in light-seconds so $c=1$ (light-second per second), dividing by $c^2$ is just dividing by one so we can ignore it, and the formula becomes $v=\frac{u+w}{1+uw}$.

It's an interesting exercise to consider what would happen if you were shining a light straight ahead - we'd set $w$ to $c$ because that's the speed of the light beam relative to you. What is its speed relative to the observer?

(Aniruddha already knows all this, I'm adding it for other people following this thread).

 

[beamie564]

w is the speed at which you throw the ball relative to you

Oops! Forgot to mention that.