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 ² = Ae k - (upward motion) k - Be (downward motion) in which A and B are constants of integration, g is the acceleration of gravity, and k = cq/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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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
o = Ae -
(upward motton)
k
o* =- Be (downmard motton)
2kr
in which A and B are constants of integration, g is the acceleration of gravity, and k = cz/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.)
个
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 o = Ae - (upward motton) k o* =- Be (downmard motton) 2kr in which A and B are constants of integration, g is the acceleration of gravity, and k = cz/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.) 个
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