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 -2kr - (upward motion) k 2 =5- Be (downward moton) %3D in which A and B are constants of integration, g is the acceleration of gravity, andk=cz/m where cz is the drag constant and m is the mass of the bullet. (Note: z is measured positive upward, and the gravitational force is assumed to be constant.)
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 -2kr - (upward motion) k 2 =5- Be (downward moton) %3D in which A and B are constants of integration, g is the acceleration of gravity, andk=cz/m where cz is the drag constant and m is the mass of the bullet. (Note: z 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
0² = Ae
k (upward motion)
=- Be (downward motton)
k
%3D
in which A and B are constants of integration, g is the acceleration of gravity, andk=cz/m
where c, 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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