When a cannon fires a projectile, neglecting air resistance, where will the velocity be greatest?

When a cannon fires a projectile, the velocity is greatest as it exits the muzzle. This occurs because the projectile is propelled forward by the high pressure generated by the explosive force within the cannon. At the moment it leaves the barrel, all the energy from the propellant has been converted to kinetic energy, resulting in the maximum velocity.

After the projectile exits the muzzle, it begins to experience the effects of gravity, which influences its trajectory and speeds in a downward motion. Although the projectile may travel significant distances and reach high points along its path, it will lose speed due to the downward pull of gravity acting on it. Consequently, while it may gain some vertical velocity as it climbs, the overall speed (the combination of horizontal and vertical velocity) will decrease until it reaches its peak height.

When it descends toward the mountainous area, its velocity will increase again due to gravity, but it will not surpass the initial exit speed obtained at the muzzle. Therefore, the moment the projectile leaves the cannon is when it achieves its highest velocity.