Explanation:
Let us assume that piece 1 is
is facing west side. And, piece 2 is
facing south side.
Let
= m and
= 2m. Hence,


= 10.5 m/s


= 10.5 m/s

= 
= 14.84 m/s
or, = 15 m/s
Hence, the speed of the third piece is 15 m/s.
Now, we will find the angle as follows.

= 
= 
= 
Therefore, the direction of the third piece (degrees north of east) is north of east.
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Answer:
2.84 m/s
Explanation:
At the top position of the circular trajectory, the normal reaction is zero:
N = 0
So it means that the only force that is providing the centripetal force is the gravitational force (the weight of the bucket). Therefore we have:

where
m is the mass of the water bucket
g = 9.8 m/s^2 is the acceleration of gravity
v is the speed of the bucket
r = 0.824 m is the radius of the circle
Solving for v,
