Answer:
a

b

Explanation:
From the question we are told that
The speed of the spaceship is 
Here c is the speed of light with value 
The length is 
The distance of the star for earth is 
The speed is 
Generally the from the length contraction equation we have that
![l = l_o \sqrt{1 -[\frac{v}{c } ]}](https://tex.z-dn.net/?f=l%20%20%3D%20%20l_o%20%20%5Csqrt%7B1%20-%5B%5Cfrac%7Bv%7D%7Bc%20%7D%20%5D%7D)
Now the when at rest the length is 
So



Considering b
Applying above equation
![l =l_o \sqrt{1 - [\frac{v}{c } ]}](https://tex.z-dn.net/?f=l%20%20%3Dl_o%20%5Csqrt%7B1%20-%20%20%5B%5Cfrac%7Bv%7D%7Bc%20%7D%20%5D%7D)
Here 
So



What’s the rest of the question or is that it?
Answer:

Explanation:
In order to solve this problem, we can do an analysis of the energies involved in the system. Basically the addition of the initial potential energy of the spring and the kinetic energy of the mass should be the same as the addition of the final potential energy of the spring and the kinetic energy of the block. So we get the following equation:

In this case, since the block is moving from rest, the initial kinetic energy is zero. When the block loses contact with the spring, the final potential energy of the spring will be zero, so the equation simplifies to:

The initial potential energy of the spring is given by the equation:

the Kinetic energy of the block is then given by the equation:

so we can now set them both equal to each other, so we get:

This new equation can be simplified if we multiplied both sides of the equation by a 2, so we get:

so now we can solve this for the final velocity, so we get:

Nuclear fusion in the core tries to blow the star apart. Gravity holds it together. Whoever designed that system really knew what he was doing. I'm kinda grateful to him.