Answer:
block velocity   v = 0.09186 = 9.18 10⁻² m/s  and speed bollet   v₀ = 11.5 m / s
Explanation:
We will solve this problem using the concepts of the moment, let's try a system formed by the two bodies, the bullet and the block; In this system all scaffolds during the crash are internal, consequently, the moment is preserved.
Let's write the moment in two moments before the crash and after the crash, let's call the mass of the bullet (m) and the mass of the Block (M)
Before the crash
      p₀ = m v₀ + 0
After the crash
     = (m + M) v
 = (m + M) v
     p₀ = 
     m v₀ = (m + M) v                    (1)
Now let's lock after the two bodies are joined, in this case the mechanical energy is conserved, write it in two moments after the crash and when you have the maximum compression of the spring
Initial
     Em₀ = K = ½ m v2
Final
     E  = Ke = ½ k x2
= Ke = ½ k x2
    Emo = E  
    ½ m v² = ½ k x²
    v² = k/m  x²
Let's look for the spring constant (k), with Hook's law
    F = -k x
    k = -F / x
    k = - 0.75 / -0.25
    k = 3 N / m
Let's calculate the speed
   v = √(k/m)   x
   v = √ (3/8.00)   0.15
   v = 0.09186 = 9.18 10⁻² m/s
This is the spped of  the  block  plus bullet rsystem right after the crash
We substitute calculate in equation  (1)
    m v₀ = (m + M) v
   v₀ = v (m + M) / m
   v₀ = 0.09186 (0.008 + 0.992) /0.008
   v₀ = 11.5 m / s
 
        
             
        
        
        
The astronaut final velocity is 0.06 m/s to the right
Explanation:
In absence of external forces, the total momentum of the box-astronaut system is conserved. 
At the beginnig, the total momentum of the two is zero, since they are at rest:

While the final momentum, after the astronaut throws the box, is:

where
m = 11 kg is the mass of the box
M = 79 kg is the mass of the astronaut
v = -0.45 m/s (to the left) is the velocity of the box (we take left as negative direction)
V is the final velocity of the astronaut
The total momentum is conserved, so

And solving , we find V:

And the positive sign indicates that the direction is to the right.
Learn more about momentum:
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#LearnwithBrainly
 
        
             
        
        
        
Upon looking around a bit I found another brainly user who asked the same question. It was answered by a user named pinkfloyde and chosen by brainly as credible. this is what the user said:
<span>"In designing electrical circuits, it is important to know the characteristics of circuits in order to know how to solve related problems that will arise whenever there will be problems in the circuits made. For example, series circuits makes the other lights go off whenever one bulb does not work. It would be easier to determine how to fix it because we know what type of circuit it is."
</span>
You should be able to use this and any other knowledge you know to come up with your desired answer
source: 
brainly.com/question/1269647
 
        
        
        
In some areas, mountains block rain, so one side may be rainy while the other is dry. the mountains create a barrier for wind as well, so the climate on one side can be warm, and cold on the other