One can set up a two-dimensional scattering theory, which could be applied to puck projectiles sliding on an ice rink and colliding with various target obstacles. The cross sectionwould be the effective width of a target, and the differential cross sectionwould give the number of projectiles scattered in the angle. (a) Show that the two-dimensional analog of (14.23 John R. Taylor) is= ||. (Note that in two-dimensional scattering it is convenient to letrange from -to.) (b) Now consider the scattering of a small projectile off a hard ‘sphere’ actually a hard disk of radius R pinned down to the ice. Find the differential cross section. (note in two dimensions hard sphere scattering is not isotropic.) (c) by integrating your answer to part (b), show that the total cross section is 2R as expected