A skateboarder with his board can be modeled as a particle of mass 76.0 kg, located at his center of mass. As shown in Figure P8.67 on page 248, the skateboarder starts from rest in a crouching position at one lip of a half-pipe (point A. The half-pipe forms one half of a cylinder of radius 6.80 m with its axis horizontal. On his descent, the skateboarder moves without friction and maintains his crouch, so that his center of mass moves through one quarter of a circle of radius 6.30 m.
(a) Find his speed at the bottom of the halfpipe (point B.
(b) Find his angular momentum about the center of curvature.
(c) Immediately after passing point B he stands up and raises his arms, lifting his center of gravity from 0.500 m to 0.950 m above the concrete (point C.)
Explain why his angular momentum is constant in this maneuver, while his linear momentum and his mechanical energy are not constant.
(d) Find his speed immediately after he stands up, when his center of mass is moving in a quarter circle of radius 5.85 m.
(e) What work did the skateboarder’s legs do on his body as he stood up? Next, the skateboarder glides upward with his center of mass moving in a quarter circle of radius 5.85 m. His body is horizontal when he passes point $, the far lip of the half-pipe.
(f) Find his speed at this location. At last he goes ballistic, twisting around while his center of mass moves vertically.
(g) How high above point does he rise?
(h) Over what time interval is he airborne before he touches down, facing downward and again in a crouch, 2.34 m below the level of point D
(i) Compare the solution to this problem with the solution to Problem 8.67. Which is more accurate?
Why? (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.)