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Hi,
Question (1), the beam of light will be travelling at the speed of light so in your spaceship yes it will catch you up at the speed of light.
Question (2), particles with mass cannot travel at the speed of light. Regardless, adding the velocities of any two objects with a velocity less than the speed of light will always give an answer less than the speed of light, no matter how close to the speed of light the objects are.
The formula for adding relativistic velocities is quite straightforward, it is
w = (u+v)/(1+ uv/c2), where c is the speed of light, u, v are the velocities to be added.
(1) Plugging in the values for everyday speeds then it is roughly u + v as uv/c2 is very small. So this agrees with everyday observation.
(2) if u and V are both c, the speed of light as in your first question then plugging in the values you get c. So this agrees with the fact that the speed of light is a constant for all observers.
(3) your second question is not quite right. Bullets cannot travel at the speed of light. Anything with mass can only approach the speed of light. Plugging in values approaching the speed of light will always give a value less than the speed of light which agrees with the fact that particles with mass can never travel faster than the speed of light.
Cheers
Paul
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