(b) Write a program to solve for the differential cross section do / do nu- merically. [Hint: My program follows the following steps. (i) Given b, find Oincident. (ii) Given (incident, find 0. (iii) Use O(b) to find |db/del. (iv) For convenience, I normalized the impact parameter b by the ra- dius R.] (c) Show that your program reproduces Eq. (14.25) when e = 1. (d) Plot the differential cross section vs. 8 for e = 0.3, 0.7 and 1.0. (e) Interpret your graph. Why does do / d shift the way it does?3. **Drag. Show that the drag force on a satellite moving with speed v in the earth's upper atmosphere is approximately fo = PAu, (1) where p is the atmospheric mass density and A is the cross-sectional area of the satellite perpendicular to the direction of the motion. Assume that the air molecules are moving slowly compared with the satellite and that their collisions with the satellite are completely inelastic. 4. ***Ineleastic bounce off a sphere. In an actual bounce off a surface, two quantities matter: the magnitude of the normal force (which is determined by the coefficient of restitution) and the magnitude of the tangential force (which is determined by the coefficient of friction). Reconsider Exam- ple 14.5 but change the nature of the bounce. Assume that the coefficient of friction is zero (as in Example 14.5) but that the coefficient of restitution 18 1 1 final = CV Linitial With 0