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.