A gun is fired straight up. Assuming that the air drag on the bullet varies quadratically with speed, show that the speed varies with height according to the equations Ae-2kx * (upward motion) - k v² = { – Be2k (downward motion in which A and B are constants of integration, g is the acceleration of gravity, and k = c2/m where c2 is the drag constan and m is the mass of the bullet. (Note: x is measured positive upward, and the gravitational force is assumed to be constant.)

College Physics
11th Edition
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Chapter1: Units, Trigonometry. And Vectors
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A gun is fired straight up. Assuming that
the air drag on the bullet varies
quadratically with speed, show that the
speed varies with height according to the
equations
v² = Ae-2kx
v² = { – Be2k (downward motion)
! (upward motion)
|
k
k
in which A and B are constants of
integration, g is the acceleration of gravity,
and k = c2/m where c2 is the drag constant
and m is the mass of the bullet. (Note: x is
measured positive upward, and the
gravitational force is assumed to be
constant.)
Transcribed Image Text:A gun is fired straight up. Assuming that the air drag on the bullet varies quadratically with speed, show that the speed varies with height according to the equations v² = Ae-2kx v² = { – Be2k (downward motion) ! (upward motion) | k k in which A and B are constants of integration, g is the acceleration of gravity, and k = c2/m where c2 is the drag constant and m is the mass of the bullet. (Note: x is measured positive upward, and the gravitational force is assumed to be constant.)
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