The circular dish, whose cross section is shown, has an outside diameter of $200$ mm$.$ A $20-$mm water jet, with a speed of $35$ m$/$s strikes the dish concentrically. The dish moves to the left at a speed of $15$m$/$s$.$The dish has a hole at its center that allows a stream of water $10$mm in diameter to pass through without resistance. The remainder of the jet at a radius of $100$ mm from the center of the dish is constant and the setup is on a horizontal XY plane. Using the basic flow equations in integral form for a control volume for the steady, incompressible, inviscid flow:

a$.$Find the velocity of the water jet at the hole and the thickness of the jet sheet at a radius of $100$ mm from the center of the dish.

b$.$Calculate the force required to maintain the dish motion.

c$.$ Write a narrative of crucial steps, important assumptions made, and all pertinent details that reflects your trough process. Think of it as if you are teaching someone else how to solve the problem.