Momentum (Conceptual) Question

Suppose there is a cannon that shoots a cannon ball at a certain angle above the horizontal (a projectile). Since momentum is conserved in both directions, the cannon should posses a velocity now in the y (or z-axis if you would like to call it) and in the x axis.

1) However, what does it mean for a cannon to be moving down into the ground?
2) Also, if a question was asked saying what is the velocity of the cannon relative to the ground, would I use use the x-velocity or the vector sum of the x and y (or z) velocities (ie get the resultant)?

Answers and Replies

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There is a normal reaction force on the canon due to the ground. thus net external force in the y direction is not zero and thus momentum in the y direction is not conserved. The canon's y velocity with respect to the ground stays zero. This is one of the constraints on the system. This, however, requires that the ground does not buckle or break under the weight of the canon. The velocity of the canon with respect to the earth should be the x velocity.

If you consider the earth in the system as well, then the total momentum will be conserved but the effect of this is not important as the mass of the earth is much larger than the canon or canon ball.