Final answer:
The drop of a bullet at 150.0 m when sighted at 100.0 m depends on projectile motion calculations involving the target distance, gravity, and muzzle velocity. A higher muzzle velocity would reduce the drop while air resistance would increase it.
Step-by-step explanation:
If a gun is sighted to hit targets at the same height and 100.0 m away, when aimed directly at a target 150.0 m away, the bullet will drop more due to gravity acting longer on it. Assuming the gun is level with the target, the time taken by the bullet to travel to the target can be found by distance = speed × time, which in this case is distance 150.0 m divided by the muzzle velocity of 275 m/s. However, to solve for how low the bullet will hit at 150.0 m, a full projectile motion calculation is required, which takes into account the additional distance, gravity, and initial velocity.
A larger muzzle velocity would mean that the bullet travels faster and thus has less time to be affected by gravity, meaning it would hit less low than with a smaller muzzle velocity. As for air resistance, the effect would be to slow down the bullet, meaning the bullet would hit even lower than without air resistance given the same muzzle velocity; but quantifying this requires knowledge of the drag coefficient and cross-sectional area of the bullet, which are not provided.