Let Now The above principles of mathematical modelling lead to the following: steps for mathematical modelling. Step 1: Identify the physical situation. Step 2: Convert the physical situation into a mathematical model by introducing parameters / variables and using various known physical laws and symbols. Step 3: Find the solution of the mathematical problem. Step 4: Interpret the result in terms of the original problem and compare the result with observations or experiments. Step 5: If the result is in good agreement, then accept the model. Otherwise modify the hypotheses/ assumptions according to the physical situation and Step 2. The above steps can also be viewed through the following diagram: Physical Introduce Mathematical go to Situation Model Solve Mathematical Interpret Solution Physical Laws and Symbols Problem Accept the Model In Good Agreement Compare with Observation Modify Hypothesis Not in Good Agreement Fig A.2.1 Example 1 Find the height of a given tower using mathematical modelling. Solution Step 1 Given physical situation is "to find the height of a given tower". Step 2 Let AB be the given tower (Fig A.2.2). Let PQ be an observer measuring the height of the tower with his eye at P. Let PQ = h and let height of tower be H. Let a be the angle of elevation from the eye of the observer to the top of the tower. not I B Fig A.2.2 Rationalised 2023-24 1=PC = QB AC H-h tan = = PC H-h H MATHEMATICAL MODELLING 199 or 1 H=h+tan a (1) Step 3 Note that the values of the parameters h. 1 and a (using sextant) are known to