Final answer:
The bullet will hit approximately 27.8 cm lower when aimed at a target 150.0 m away. A larger muzzle velocity would result in a longer range for the gun, but air resistance would have a greater effect on the bullet's trajectory.
Step-by-step explanation:
To find how low the bullet will hit when aimed directly at a target 150.0 m away, we can use the concept of projectile motion. The bullet will experience both horizontal and vertical motion. Since the target is higher than the original height of the gun, the bullet will hit lower. We can calculate the vertical displacement using the equation:
Vf² = Vi² + 2aΔy
where Vf is the final velocity in the y-direction, Vi is the initial velocity in the y-direction, a is the acceleration due to gravity, and Δy is the vertical displacement. Solving for Δy, we find that the bullet will hit approximately 27.8 cm lower when aimed at a target 150.0 m away from the gun.