To determine the coefficient of kinetic friction for a 4.00 kg block pushed along the ceiling with an 85.0 N force at a 55.0° angle, the net force acting on the block must be calculated. The applied force can be broken down into horizontal and vertical components, with the vertical component affecting the normal force. The block accelerates at 6.00 m/s², allowing the net force to be derived from Newton's second law. The direction of the kinetic friction force opposes the motion of the block, acting to the left. Understanding these forces and their interactions is crucial for solving the problem effectively.