2.12 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 -2kx = Ae (upward motion) k | 12 = - Be2k (downward motion) 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.)
2.12 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 -2kx = Ae (upward motion) k | 12 = - Be2k (downward motion) 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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Transcribed Image Text:2.12
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 _ g
* (upward motion)
k
2² = - Be2k* (downward motion)
k
in which A and B are constants of integration, g is the acceleration of gravity, and k = c2/m
where cz 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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