Answer:
Approximately 
, assuming that the rocket had no propulsion onboard, and that air resistance on the rocket is negligible.
Explanation:
Initial velocity of this rocket: 
.
When the rocket is at its maximum height, the velocity of the rocket would be equal to 
. That is: 
.
The acceleration of the rocket (because of gravity) is constantly downwards, with a value of 
.
Let 
denote the distance that the rocket travelled from the launch site to the place where it attained maximum height. The following equation would relate 
to 
, 
, and 
:
.
Apply this equation to find the value of :
.
In other words, the maximum height that this rocket attained would be 
.
Again, assume that the air resistance on this rocket is negligible. The rocket would return to the ground along the same path, and would cover a total distance of 
.
Answer: A (smooth)
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The answer should be B. According to the conservation of energy, the energy cannot be created nor destroyed, but it can be transformed. Since the object is moving down, that means its height is decreasing, causing the potential energy decreasing and the kinetic energy increasing to fulfill the conservation law.
