# Observer Sees When I Throw Ball at Speed of Light

• B
• jirakst

#### jirakst

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

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?

• 