Since there are no choices, then this question calls for open-ended answers. Facts-based science must have proven underlying laws that support inferences such as Coulomb's Law, Kinetic Theory of Matter and many more. On the other hand, examples of science that focus on personal belief is philosophy. This depends on the perspective of known philosophers. An example would be Sigmund Freud who proposed the theory of 3 personalities. Although it is more on personal beliefs, this is used as a foundation in the study of psychology.
Answer:
Part a)

Part b)

Part c)

Part d)

Explanation:
Part a)
While bucket is falling downwards we have force equation of the bucket given as

for uniform cylinder we will have

so we have


now we have




now we have


Part b)
speed of the bucket can be found using kinematics
so we have



Part c)
now in order to find the time of fall we can use another equation



Part d)
as we know that cylinder is at rest and not moving downwards
so here we can use force balance



mass of the bottle in each case is M = 0.250 kg
now as per given speeds we can use the formula of kinetic energy to find it
1) when speed is 2 m/s
kinetic energy is given as


2) when speed is 3 m/s
kinetic energy is given as


3) when speed is 4 m/s
kinetic energy is given as


4) when speed is 5 m/s
kinetic energy is given as


5) when speed is 6 m/s
kinetic energy is given as


Answer:
The pressure after passing the valve is 23,8 [Kpa] ( 0,234 atm) and the pressure drop is about 1,53 [Kpa]
Explanation:
We need to use the formula of bernoulli, in the attached image we can see the fluid throw the pipe, we also can calculate the velocity inside the pipe using the flow rate and the cross sectional area.
For this case, we don't use the elevation difference and therefore those terms can be cancelled.
When the area has reduced the velocity of the fluid is increased but there is a drop pressure through the valve.