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So, for example, we have the planet, a spaceship (cylinder shaped) and a ball in it (spaceship is like transparent so we can see the ball). We are on the planet looking at the ship. The spaceship moves the speed of light and the ball with it. But what if the ball was moving, for example, 50000 km/h in the ship? It should still be moving the speed of light to us, but would it go through the ship?

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As Bubble said, the ship in your experiment can't travel at the speed of light. More precisely, the ship could travel at the speed of light if it would be massless. But in that circumstance the ship can't constitute a reference frame on which define a relative motion of a ball; you can't think about the ship at rest and measure the relative motion of the ball in it. Likewise, you can't think about photons at rest. This kind of errors occurs thinking about objects moving at the speed of light from the point of view of non-relativistic cinematic, where speed simply adds.

In Special Relativity you have the Lorentz factor $$\gamma(v)=1\big/{\sqrt{1-\tfrac{v^2}{c^2}}}$$ which describes the transformation from the quantities as measured in one reference frame to those measured in another reference frame moving at speed $v$ with respect to the other. As you can see, if $v=c$ the factor $\gamma(v)$ turns out to be ${1\over 0}$ (or infinity, if you prefer) and you can't perform any transformation between this two frames.

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Your error is in the assumption that the ship can move at the speed of light. It can't. If you replace "ship" with "beam of light" then a ball can't be traveling on it and if you go further and replace "ball" with "another beam of light" then you just have two beams of light.

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As the ship gets closer to the speed of light, according to a stationary observer, the ships length will get shorter, and time in the ship slows down.

It is impossible for a ship to reach the speed of light, but even if it were possible, the time would be frozen in the ship relative to the stationary observer due to time dilation. Therefore because time is frozen, it would be impossible for the observer to see the ball moving within the ship, not to mention the ship would have 0 length anyway due to length contraction.

But all this aside, the ship can never reach the speed of light.

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