44.1 meters initial height of the rock.
 
        
             
        
        
        
Refer to the diagram shown below.
T = the tension in the rope
N = the the normal reaction (the force that the table exerts on the box)
W = the hanging weight
Assume that the pulley is frictionless.
For equilibrium,
T = W
and
T + N = 77
Therefore
N = 77 - W
(a) When W = 30 N,
 N = 77 - 30 = 47 n
 Answer: 47 N
(b) When W = 60 N,
 N = 77 - 60 = 17 N
 Answer: 17 N
(c) When W = 90 N
 N = 77 - 90 = - 13 N
There is no normal reaction, and the system is no longer in equilibrium.
Instead, the box will be lifted by a force of 13 N, and the box will accelerate upward.
 
        
        
        
The change in the kinetic energy refers to the work done in displacing a body, thus, the change in the kinetic energy of an object refers to the work done on the object.
The correct formula to use is:
W = Initial kinetic energy - Final kinetic energy;
Where, W = change in kinetic energy
Final kinetic energy and initial kinetic energy = 1/2 MV^2
Initial velocity = 15 m/s
Final velocity  = 13.5 m/s
Initial mass = 0.650 kg
Final mass = 0.950 kg
W = 1/2 [0.650* (15 *15)] - 1/2 [0.950 * (13.5 * 13.5)]
W = 146.25 - 173.13 = 26.88
Therefore, the change in kinetic energy is 26.88 J.
 The negative sign has to be ignored, because change in kinetic energy can not be negative.
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7. solar flare: f.
8. core: h.
9. chromosphere: b.
10. sunspot: d.
11. corona: c.
12. nuclear fusion: j.
13. photosphere: a.
14. solar wind: g.
15. prominence: e.
16. radiation zone: k.
17. convection zone: i.