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Homework Help: Analytical Mechanics question

  1. Nov 2, 2011 #1
    A cannon launches a 10cm diameter cannonball w/ a muzzle velocity of 100 m/s horizontally from the top of a 40m high wall under STP. The cannon has a mas of 40 kg and is free to recoil.
    a. What is the initial v of the cannonball wrt the ground
    b.calculate the landing position neglecting air resistance.
    c. calculate landing position considering air resistance.
    d. calculate landing position if the same event happens on planet x, which is 3 times the Earth's mass and twice its radius. Furthermore, the viscosity of planet X's atmosphere is 1Ns/m^2 and the density of its atmosphere is 1 kg/m^3. Which form of drag is stronger, linear or quadratic. For your landing calculation, ignore the weaker of the drag forces.

    I am just starting this and my only question at the moment is, does the fact that the cannon is free to recoil affect the muzzle velocity and there for the landing position of the cannonball? I

    I'll add more as I solve it.

    Thanks guys,
  2. jcsd
  3. Nov 3, 2011 #2
    Interesting because the density of the cannon ball is not provided. Yes, velocity of the projectile relative to the cannon is affected by the recoil. The analogy is two billard balls on either end of a compressed spring compared to one billard ball compressing the spring to the same extent with the opposite end fixed. With the latter situation the billard ball will have a greater speed because all the potential energy of the spring goes into one ball.

    In the old days cannon balls were made of iron. But some were hollow and filled with black powder.
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