Question

Consider an iron cannonball of diameter 15 ?? and density 7.8 ?/??3, that is fired with an initial velocity of 300 ?/? at an angle of 50∘ above the horizontal. The air resistance is approximately quadratic, however, since it is proportional to the atmospheric density and the density falls off exponentially with height, the air resistance is ? = ?(?)?2 where,

?(?) = ??2e−?/?and ? = 0.25 ??2/?4 and ? ≈ 10,000 ?.

Determine the equations of motion for the cannonball. Then write a computer program to solve the equations numerically to find the horizontal and vertical trajectories, ?(?) and ?(?). Plot the cannonball’s trajectory for the time interval 0 < ? < 35 ? and find its horizontal range. Finally, determine the trajectory for the case where you ignore the change in atmospheric density but include air resistance, and the case where you ignore air resistance completely.

Answer 1