I need help with these two questions:
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:
v^2 = Ae^-2kx - g/k (upward motion)
v^2 = g/k - Be^2kx (downward motion)
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).
This solution contains detailed step-by-step calculations to show that the speed varies with height of the bullet and also the displacement of the particle passing through the origin.
Momentum and projectile motion.
A shell is fired from a gun with a muzzle velocity of 14 m/s, at an angle of 60° with the horizontal. At the top of the trajectory, the shell explodes into two fragments of equal mass (Fig. 9-30). One fragment, whose speed immediately after the explosion is zero, falls vertically. How far from the gun does the other fragment land, assuming that the terrain is level and that the air drag is negligible?View Full Posting Details