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 p² = Ae-2k - (upward motion) k o² = - Bek k (downward motion) in which A and B are constants of integration, g is the acceleration of gravity, and k = cg/m where cą 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.) %3D
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 p² = Ae-2k - (upward motion) k o² = - Bek k (downward motion) in which A and B are constants of integration, g is the acceleration of gravity, and k = cg/m where cą 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.) %3D
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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
k
- (upward motion)
o² =- Bek (downward motion)
k
in which A and B are constants of integration, g is the acceleration of gravity, andk = cz/m
where cą 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.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F340e30c0-0842-4054-806c-7f19e9c06292%2F06ff94b5-6bff-40da-8c06-fb13eddbbb8e%2Fx1the4l_processed.jpeg&w=3840&q=75)
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
k
- (upward motion)
o² =- Bek (downward motion)
k
in which A and B are constants of integration, g is the acceleration of gravity, andk = cz/m
where cą 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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