text: I assume opposite side of canyon is level with the one where he starts and there is no air resistance.\n\na)  x is the speed. \nHorizontal component is x*cos(15) and vertical - x*sin(15). \nThe time it will take him to go 12 meters horisontally is 12/(x*cos(15)) \nThe time to go up and down to same level is 2*x*sin(15)/9.8\nYou want the two to be equal, so you need to solve:\n  2*x*sin(15)/9.8 = 12/(x*cos(15))\n x=square_root[ 6*9.8 / (sin(15)cos(15)) ]\n\nb) his speed will be same as in a), with vector pointing 15 degres down.