Answer:
T = 764.41 N
Explanation:
In this case the tension of the string is determined by the centripetal force. The formula to calculate the centripetal force is given by:
(1)
m: mass object = 2.3 kg
r: radius of the circular orbit = 0.034 m
v: tangential speed of the object
However, it is necessary to calculate the velocity v first. To find v you use the formula for the kinetic energy:

You have the value of the kinetic energy (13.0 J), then, you replace the values of K and m, and solve for v^2:

you replace this value of v in the equation (1). Also, you replace the values of r and m:

hence, the tension in the string must be T = Fc = 764.41 N
Answer:
Part a)

Part b)

Part C)


Part d)
In horizontal direction velocity will remain constant

in vertical direction we have

Explanation:
Part a)
Horizontal speed of the cannon

angle of projection

now we have
horizontal speed = 
vertical speed = 
now the time taken by it to cover the distance 100 m from the wall



Part b)
Since it hits the ground in the same time
so the height of the castle is given as



Part C)
At highest point of the projection
the vertical component of the velocity will become zero
so we will have


Part d)
In horizontal direction velocity will remain constant
so we have

in vertical direction we have



Part e)
The work done is equal to the change in potential energy which is:
P.E = mgh
P.E = 500 x 9.81 x 15
P.E = 73,575 J
Power = work / time
Power = 73,575 / 20
Power = 3,700 Watts