(a) 5.66 m/s
The flow rate of the water in the pipe is given by

where
Q is the flow rate
A is the cross-sectional area of the pipe
v is the speed of the water
Here we have

the radius of the pipe is
r = 0.260 m
So the cross-sectional area is

So we can re-arrange the equation to find the speed of the water:

(b) 0.326 m
The flow rate along the pipe is conserved, so we can write:

where we have

and where
is the cross-sectional area of the pipe at the second point.
Solving for A2,

And finally we can find the radius of the pipe at that point:

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Explanation:
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The block's velocity is determined as 10.03 m/s.
<u>Explanation:</u>
According to work energy theorem, the work done on an object is equal to the change in kinetic energy of the object.
So, work done = Kinetic energy

Thus, the velocity can be determined as


Velocity = 10.03 m/s.
So the block's velocity is determined as 10.03 m/s.