Answer:
38.4 m/s
Explanation:
a) at t = 3.2s. 
b) at t = 3.2 + Δt. 
c) As Δt approaches 0. We can find the velocity by the ratio of Δx/Δt






As Δt approaches 0, v = 38.4 + 0 = 38.4 m/s
To solve this problem it is necessary to apply the concepts related to the flow as a function of the volume in a certain time, as well as the potential and kinetic energy that act on the pump and the fluid.
The work done would be defined as

Where,
PE = Potential Energy
KE = Kinetic Energy

Where,
m = Mass
g = Gravitational energy
h = Height
v = Velocity
Considering power as the change of energy as a function of time we will then have to


The rate of mass flow is,

Where,
= Density of water
A = Area of the hose 
The given radius is 0.83cm or
m, so the Area would be


We have then that,



Final the power of the pump would be,



Therefore the power of the pump is 57.11W
Answer:
Part a)
h = 0.86 cm
Part b)
Level will increase
Explanation:
Part a)
Mass of the ice cube is 0.200 kg
Now from the buoyancy force formula we know that weight of the ice is counter balanced by buoyancy force on the ice
So here we will have



now as we know that ice will melt into water
so here volume of water that will convert due to melting of ice is given as


So here extra volume that rise in the level will be given as



Part b)
Since volume of water that formed here is more than the volume that is displaced by the ice so we can say that level of liquid in the cylinder will increase due to melting of ice