AP Free Response Question
2005 C1
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A ball of mass
M
is thrown vertically upward with an initial speed of
v
_{o}
. 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
,
v
_{o}
, 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
t
_{f}
is the time at which the ball returns to the height from which it was thrown.
Topic Formulas
Description
Published Formula
angular displacement
angular momentum
angular velocity
center of mass
centripetal acceleration
friction
gravitational force (vector)
gravitational potential energy
Hooke's Law
impulse
kinetic energy
linear momentum
linear velocity and angular velocity
moment of inertia
net torque
Newton's 2nd Law
Newton's Law of Universal Gravitation
period and frequency
period of a simple pendulum
period of a spring
potential elastic energy
potential energy
power (dot product)
rate of change of momentum
rate of change of work
rotational kinetic energy
torque
uniform acceleration  displacement and instantaneous velocity
uniform acceleration  instantaneous position
uniform acceleration  instantaneous velocity
work (dot product)
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