A skateboarder with his board can be modeled as a particle of mass 76.0 kg, located at his center of mass (which we will study in Chapter 9 ). As in Figure $\mathrm{P} 8.67$ , the skate-boarder starts from rest in a crouching position at one lip of a half-pipe (point A). The half-pipe is a dry water channel, forming one half of a cylinder of radius 6.80 $\mathrm{m}$ with its axis horizontal. On his descent, the skateboarder moves without friction so that his center of mass moves through one quarter of a circle of radius $6.30 \mathrm{m} .$ (a) Find his speed at the bottom of the half-pipe (point $(B)$ . (b) Find his centripetal acceleration. (c) Find the normal force $n_{\mathrm{B}}$ acting on the skateboarder at point ${B}$ . Immediately after passing point $(B),$ he stands up and raises his arms, lifting his center of mass from 0.500 $\mathrm{m}$ to 0.950 $\mathrm{m}$ above the concrete (point C). To account for the conversion of chemical into mechanical energy, model his legs as doing work by pushing him vertically up, with a constant force equal to the normal force $n_{\mathrm{B}},$ over a distance of 0.450 $\mathrm{m}$ . (You will be able to solve this problem with a more accurate model in Chapter $11 . )$ (d) What is the work done on the skate-boarder's body in this process? Next, the skateboarder glides upward with his center of mass moving in a quarter circle of radius 5.85 $\mathrm{m}$ . His body is horizontal when he passes point ${D}$ , the far lip of the half-pipe. (e) Find his speed at this location. At last he goes ballistic, twisting around while his center of mass moves vertically. (f) How high above point ${D}$ does he rise? (g) Over what time interval is he airborne before he touches down, 2.34 $\mathrm{m}$ below the level of point $D$ [ Caution: Do not try this yourself without the required skill and protective equipment, or in a drainage channel to which you do not have legal access.]