PhysicsLAB AP Free Response Question
2005 C1

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A ball of mass M is thrown vertically upward with an initial speed of vo. It experiences a force of air resistance given by F = —kv, where k is a positive constant. The positive direction for all vector quantities is upward.
 
Express all algebraic answers in terms of M, k, vo, and fundamental constants.
 
 (a) Does the magnitude of the acceleration of the ball increase, decrease, or remain the same as the ball moves upward? Justify your answer.

 (b) Write, but do NOT solve, a differential equation for the instantaneous speed v of the ball in terms of time t as the ball moves upward.

 (c) Determine the terminal speed of the ball as it moves downward.

 (d) Does it take longer for the ball to rise to its maximum height or to fall from its maximum height back to the height from which it was thrown? Justify your answer.

 
(e) On the axes below, sketch a graph of velocity versus time for the upward and downward parts of the ball’s flight, where tf  is the time at which the ball returns to the height from which it was thrown.
 




 
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