Exercise 2: Accuracy of Computational Model: Velocity vs. TimeSince the computational approach is based on an approximation, it is important todetermine just how small 𝛥𝑡 should be for the approximation to accurately solve the1D air resistance problem. Make a comparison between the time dependence of thevelocity predicted by the computational model, and that predicted by the exactresult,𝑣! (𝑡) = 2𝑚𝑔𝐷𝜚𝐴 tanh 𝐷𝜚𝐴𝑔2𝑚 𝑡 .Use parameters that describe a 16-‐pound bowling ball (you should look up the diameter, and convert to meters), and let it fall a distance equivalent to the height ofthe Sears, oops -‐ Willis, tower (440 m). Assume the ball is initially at rest. Use a value of 0.5 for the drag coefficient, and the density of air near sea level. What valueof 𝛥𝑡 do you deem to be sufficiently small for the computational model to be accurate? Explain how you arrived at this value of 𝛥𝑡 . Exercise 3: Accuracy of Computational Model: Position vs. TimeCarry out the same comparison (computational vs. exact analytical solution) for thebowling ball's position as a function of time. The exact result for the ball's position isgiven by𝑦(𝑡) = 2𝑚𝐷𝜚𝐴 ln cosh 𝐷𝜚𝐴𝑔2𝑚 𝑡 .Assume the bowling ball is falling the same distance of 440 m. Do you find the samevalue of 𝛥𝑡, as found for the velocity comparison of Exercise 2, to be acceptable forthe position comparison? Exercise 4: Position and Velocity of Dropped Bowling Ball Produce plots of the bowling ball's velocity and vertical position as functions of time from the results of the computational model, using the parameters from the previous exercises and the value ofDelta t(determined in Exercises 2 and 3) that produces a tolerably accurate computational solution. Has the bowling ball reached its terminal velocity by the time it hits the ground? Use your model to predict the time required for the bowling ball to fall the full 440 meters to the ground.
Exercise 4:Position and Velocity of Dropped Bowling Ball Produce plots of the bowling ball's velocity and vertical position as functions of time from the results of the computational model, using the parameters from the previous exercises and the value of At (determined in Exercises 2 and 3) that produces a tolerably accurate computational solution.Has the bowling ball reached its terminal velocity by the time it hits the ground? Use your model to predict the time required for the bowling ball to fall the full 440 meters to the ground.