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A gun is fired straight up from the origin with initial speed vo. Assuming that the air drag on the bullet varies quadratically with speed (c2 v³). For upward motion of the bullet: a) Apply Newton's second law on the bullet in air, and write the differential equation of motion. b) Write the expression relating dv, v, dx, g, cz and m. c) Show that the speed varies with height according to the equations. v² = Ae-2kx - (upward motion) in which A and B are constants of integration, g is the acceleration of gravity, and k = cy/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.)

A gun is fired straight up from the origin with initial speed vo. Assuming that the air drag on the bullet varies quadratically with speed (c2 v³). For upward motion of the bullet: a) Apply Newton's second law on the bullet in air, and write the differential equation of motion. b) Write the expression relating dv, v, dx, g, cz and m. c) Show that the speed varies with height according to the equations. v² = Ae-2kx - (upward motion) in which A and B are constants of integration, g is the acceleration of gravity, and k = cy/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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physics mechanics
A gun is fired straight up from the origin with initial speed vo. Assuming that the air drag on the bullet varies quadratically with speed (c2 v²). For upward motion of the bullet: a) Apply Newton's second law on the bullet in air, and write the differential equation of motion. b) Write the expression relating dv, v, dx, g, cz and m. c) Show that the speed varies with height according to the equations. v? = Ae-2kx - (upward motion) in which A and B are constants of integration, g is the acceleration of gravity, and k = cy/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.) d) Explain what will change yhen the bullet is moving downward
Transcribed Image Text:A gun is fired straight up from the origin with initial speed vo. Assuming that the air drag on the bullet varies quadratically with speed (c2 v²). For upward motion of the bullet: a) Apply Newton's second law on the bullet in air, and write the differential equation of motion. b) Write the expression relating dv, v, dx, g, cz and m. c) Show that the speed varies with height according to the equations. v? = Ae-2kx - (upward motion) in which A and B are constants of integration, g is the acceleration of gravity, and k = cy/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.) d) Explain what will change yhen the bullet is moving downward
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