QZ_01_S

# QZ_01_S - Ph1a Solution to Quiz 1 Alejandro Jenkins Fall...

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Ph1a: Solution to Quiz 1 Alejandro Jenkins, Fall 2004 Problem 1 (6 points) - Marble Descending Staircase 1 A marble bounces regularly down a long ﬂight of stairs, hitting each step with the same speed and at the same distance from the edge, and then bouncing up to the same height h above the step, as shown in the ﬁgure. l l h v v i f Each stair has the same height and depth ` . The horizontal component of the marble’s velocity is constant throughout, but the stairs have the property that - v f /v i = e , where v i and v f are the vertical velocity components just before and just after the bounce respectively, and e is a constant (0 < e < 1). (a) (2 points) Find an expression for v i in terms of e , ` , and the gravitational accelera- tion g . Solution: The marble bounces oﬀ the stair and begins moving upward with a vertical velocity v f = - ev i . After reaching the top of its bounce, it begins to move downward. When it passes the level of the previous stair, it will have vertical velocity

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QZ_01_S - Ph1a Solution to Quiz 1 Alejandro Jenkins Fall...

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