Final answer:
The question involves calculating how much lower a bullet will hit if aimed at a target further than the distance it is sighted for, taking into consideration gravity, muzzle velocity, and air resistance in the field of Physics.
Step-by-step explanation:
The question addresses the principles of projectile motion in Physics, particularly related to firearms. In part (a), when a gun is sighted to hit targets 100 meters away, and it's fired at a target 150 meters away without adjusting the aim, the bullet will hit lower due to gravity affecting it over the increased distance. The muzzle velocity of the bullet, which is 275 m/s, is crucial for calculating the drop. However, the exact amount of drop cannot be calculated without considering the time of flight or the ballistic coefficient of the bullet.
For part (b), a larger muzzle velocity would translate to a shorter time of flight at a given range, thereby reducing the effect of gravity and causing the bullet to hit less low. Moreover, air resistance would slow the bullet down, increasing the time the force of gravity has to act on it, leading to a lower point of impact at further distances.