Final answer:
Gun sights are adjusted for gravity, and a bullet aimed at a 150 m target with a gun sighted for 100 m will hit lower. A higher muzzle velocity would decrease the bullet's drop, while air resistance would reduce its range and speed. The maximum projectile range is ideally achieved at a 45-degree launch angle but is reduced by air resistance.
Step-by-step explanation:
Projectile Motion and the Muzzle Velocity:
When considering projectile motion, such as a bullet fired from a gun, gun sights are calibrated to allow for gravity's pull. If the gun is sighted for a 100.0 m target, but aimed directly at a target 150.0 m away without adjusting the aim, the bullet will hit lower than the target due to gravity pulling it down over the longer distance. The muzzle velocity, in this case, is 275 m/s. A higher muzzle velocity would mean the bullet travels faster and would thus decrease the time gravity has to act on it, meaning it would hit less low relative to the target at the same distance. Additionally, air resistance can slow down the bullet, reducing its range and speed, causing further deviation from the intended target.
The maximum effective range of a projectile is also influenced by the launch angle. At 45 degrees, and ignoring air resistance, the range is maximized, but the ideal angle shifts slightly lower when air resistance is taken into account. The same range can occur for two angles that add up to 90 degrees, albeit with different maximum heights achieved during flight.