Answer :

Final answer:

When a gun sighted to hit a target at 100 meters is used to aim at a target 150 meters away, the bullet will hit approximately 0.651 meters below the intended point. A larger muzzle velocity would decrease the bullet's drop by allowing it to reach the target faster. Considering air resistance would increase the bullet's drop by slowing its horizontal velocity.

Explanation:

When a gun is sighted to hit a target at 100 meters, and the same sighting is used to aim at a target 150 meters away, the bullet will hit lower than intended. To determine how low the bullet will hit, we need to calculate the time it takes for a bullet to travel 100 meters and then calculate its vertical displacement when it travels 150 meters.

First, we find the time it takes for the bullet to reach 100 meters. Since the horizontal velocity is constant (air resistance is ignored), we use the formula:

Horizontal Distance (Dx) = Horizontal Velocity (Vx) * Time (t)

t = Dx / Vx

t = 100.0 m / 275 m/s ≈ 0.364 s

Next, we use this time to calculate the vertical displacement at 150 meters, using the formula:

Vertical Displacement (Dy) = [tex]Viy * t + (1/2) * g * t^2[/tex]

Since the initial vertical velocity (Viy) is 0 for horizontal fire, and g is the acceleration due to gravity (9.8 m/s^2), we have:

Dy = [tex](1/2) * g * t^2[/tex]

Dy =[tex](1/2) * 9.8 m/s^2 * (0.364 s)^2[/tex]

The bullet would thus hit approximately 0.651 meters (65.1 cm) below the target's height at 150 meters.

Concerning how a larger muzzle velocity would affect this problem: A larger muzzle velocity would result in the bullet reaching the target faster, which means less time for gravity to act on it, hence, it would hit less low. On the matter of air resistance, if factored in, it would slow down the bullet, increasing the time it takes to reach the target and thus increasing the vertical displacement.

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Rewritten by : Barada