Answer:
The acceleration of
is 
Explanation:
From the question we are told that
The mass of first block is 
The angle of inclination of first block is 
The coefficient of kinetic friction of the first block is 
The mass of the second block is 
The angle of inclination of the second block is 
The coefficient of kinetic friction of the second block is 
The acceleration of
are same
The force acting on the mass
is mathematically represented as

=> 
Where T is the tension on the rope
The force acting on the mass
is mathematically represented as


At equilibrium

So

making a the subject of the formula

substituting values 
=> 
Answer:
a) m = 69.0 kg
b) release some gas in the opposite direction to the astronaut's movement
Explanation:
a) Let's use Newton's second law
F = m a
m = F / a
m = 60.0 / 0.870
m = 69.0 kg
b) when we exert a force on the astronaut it acquires a momentum po, as the astronaut system plus spacecraft is isolated, the momentum is conserved
p₀ = p_f
m v = M v '
v ’=
so we see that the ship is moving backwards, but since the mass of the ship is much greater than the mass of the astronaut, the speed of the ship is very small.
One method to avoid this effect is to release some gas in the opposite direction to the astronaut's movement so that the initial momentum of the astronaut plus the gas is zero and therefore no movement is created in the spacecraft.