A 70 kg skateboarder wants to just make it to the upper edge of a \"half pipe,\"

Question

A 70 kg skateboarder wants to just make it to the upper edge of a "half pipe," with a radius r, of 2.3 m as shown in the figure below. What speed vidoes he need at the bottom if he is to coast all the way up?

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

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

Explanation / Answer

use the law of consevation of energy at top and bottom positions

Total Eenrgy at bottom = total energy at top

KEb + PEb = KE t + PE t

0.5 mv i^2 + 0 = 0 + m g h

vi^2 = 2 g h

vi^2 = 2* 9.81 *   2.3

Vi = 6.717 m/s is the velocity at the bottom

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nOw use for height h = r- 0.75

h = 2.3 - 0.75

h = 1.55 m

thus

v^2 = 2* 9.81 * 1.55

vi = 5.51 m/s

initial velcoty needed to the upper edge is 5.51 m/s

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