Final answer:
The bullet will hit the ground approximately 0.0166 seconds later and about 1.5 meters below the line of sight when aimed directly at a target 150.0 m away.
Step-by-step explanation:
To determine how low the bullet will hit if aimed directly at a target 150.0 m away, we need to analyze the vertical motion of the bullet. We can use the equation h = v^2 / (2g), where h is the maximum height, v is the initial vertical velocity, and g is the acceleration due to gravity. Given that the maximum height is 409 meters, we can rearrange the equation to solve for the initial vertical velocity: v = sqrt(2gh).
Plugging in the values, v = sqrt(2 * 9.8 * 409) = 90.42 m/s. Now, we can use the equation d = vt, where d is the vertical distance and t is the time of flight. Since the bullet will hit the ground at the same height as the gun (1.5 meters), we can solve for t: t = d / v = 1.5 / 90.42 = 0.0166 seconds.
Therefore, if the bullet is aimed directly at a target 150.0 m away, it will hit the ground approximately 0.0166 seconds later and about 1.5 meters below the line of sight.