Problem -
Tom cat is chasing Jerry mouse the initial distance between them is S0 = 100m. Tom runs Vc = 4-at m/s (negative accident) Jerry's velocity depends on the distance between Tom& Jerry V = Vmax - Ks (3-0.025 m/s), ds/ds = Vm - Vc = -1-025 +at m/s.
1. Find the true solution. Plot it to find when will Tom catch Jerry with a = 0.01 m/s2.
2. If a = 0.01 m/s2, use 4th order Runge-Kutta method to compute when will Tom catch Jerry. Use a step size so that you result reasonably accurate compared with the true solution.
3. Use Adam-Bashforth Technique with your result from Runge-Kutta method as initial step to compute when will Tom catch Jerry.
4. Suppose Tom's acceleration is unknown someone found did not catch Jerry in 2 minutes. Is it possible Tom will catch Jerry in his life time?