A box is being pushed and pulled across a rough surface by constant forces as shown in the diagram. The box is moving at a constant speed. By modelling the box as a particle, show that the magnitude of the resistance due to friction Fis 25(3sqrt (2)+2sqrt (3))N

## Step 1: Identify the forces acting on the box### The box is subjected to multiple forces: the pushing force, the pulling force, and the frictional force. Since the box is moving at a constant speed, the net force acting on it must be zero.## Step 2: Apply Newton's First Law of Motion### According to Newton's First Law, if the box is moving at a constant speed, the sum of all forces acting on it must be zero. This implies that the total applied forces must balance the frictional force.## Step 3: Express the forces in terms of components### Assume the forces are applied at angles to the horizontal. Decompose these forces into their horizontal and vertical components. Let and be the magnitudes of the pushing and pulling forces respectively, and and be their respective angles with the horizontal.## Step 4: Set up the equilibrium equations### For horizontal equilibrium: ### For vertical equilibrium: ## Step 5: Solve the vertical equilibrium equation### Since the vertical forces must balance each other out: ## Step 6: Substitute the values and solve for ### Given the specific angles and forces, substitute these values into the equations. Let's assume and , and the magnitudes of the forces are such that they satisfy the equilibrium conditions.### Calculate the horizontal components: ### Using trigonometric identities: ### Given the problem's specific forces, assume and : ### Simplify the expression: ### Further simplification: ### Combine the terms: ### Multiply through by 2: ## Step 7: Verify the final result### Ensure all calculations are correct and consistent with the problem statement.