Help walk me though this

program it using python

In class you learned that the ODE describing the velocity gained by a falling body is gm du dt (1) e For a body of mass m, acceleration of gravity g, and drag coefficient c. The closed form solution of the equation is v(t) = (1 e-(c/mt) = u(1-c-e/m)) (2) is the terminal velocity. C where UT We also learned in class that the velocity of the ball can be iteratively calculated by numerically solving the ODE using the formula C v(ti+1) = v(ti) + (g- ult;))At = v(ti) + (g -u(ta))(t+1 t) (3) m 2012 a where v(t+1) is velocity of the body at time ti+1, and v(ta) at time t. At is size of the time-step, and the above equation works for a small enough time-step size. Write a program to calculate the velocity of the body at different time, as it accelerates to it's terminal velocity, using equation (3). You can assume g = 10, m = 10 and c = 50. (a) Plot the variation of velocity in time. (b) What is the maximum time-step size At that allows accurate calculation of the velocity ? (c) Will the maximum allowable time-step size At change if the mass of the body (m) increases to 100 ? (d) Theoretically, the falling body will take time t = a to reach terminal velocity (vr). Using the program, calculate the time required by the body to attain 99.99 percent of the terminal velocity (ur) m =