A \(55 \mathrm{~kg}\) skateboarder wants to just make it to the upper edge of a "half-pipe" with a radius of \(3.0 \mathrm{~m}\), as shown in Figure P10.55. What speed \(v_{\mathrm{i}}\) does he need at the bottom if FIGURE P10.55 he is to coast all the way up?

a. First do the calculation treating the skateboarder and board as a point particle, with the entire mass nearly in contact with the half-pipe.

b. More realistically, the mass of the skateboarder in a deep crouch might be thought of as concentrated \(0.75 \mathrm{~m}\) from the half-pipe. Assuming he remains in that position all the way up, what \(v_{\mathrm{i}}\) is needed to reach the upper edge?

Transcribed Image Text:

FIGURE P10.55 3.0 m