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
Now the when at rest the length is
So
Considering b
Applying above equation
Here
So
(a)
The total mechanical energy of the space probe must be constant, so we can write:
(1)
where
is the kinetic energy at the surface, when the probe is launched
is the gravitational potential energy at the surface
is the final kinetic energy of the probe
is the final gravitational potential energy
Here we have
at the surface, (radius of the planet),
(mass of the planet) and m=10 kg (mass of the probe), so the initial gravitational potential energy is
At the final point, the distance of the probe from the centre of Zero is
so the final potential energy is
So now we can use eq.(1) to find the final kinetic energy:
(b)
The probe reaches a maximum distance of
which means that at that point, the kinetic energy is zero: (the probe speed has become zero):
At that point, the gravitational potential energy is
So now we can use eq.(1) to find the initial kinetic energy: