A hunter aims horizontally at a target 120 m away. If the bullet leaves the gun at a speed of 250 m/s, by how much will it miss the target?

The bullet drops by an amount (1/2)g t^2 below the target. t is the time of flight, 120m/250 m/s = 0.48 s

To determine how much the bullet will miss the target, we need to consider the horizontal motion of the bullet and the vertical motion due to the effect of gravity.

First, let's find the time it takes for the bullet to reach the target using the formula:

time = distance / velocity

The distance is given as 120 m, and the velocity of the bullet is 250 m/s. So we have:

time = 120 m / 250 m/s

Calculating this, we find that the bullet takes 0.48 seconds to reach the target.

Next, we'll find the vertical displacement of the bullet during this time. The vertical motion of the bullet can be determined using the equation of motion:

distance = initial velocity * time + (1/2) * acceleration * time^2

In this case, the initial vertical velocity is zero (since the bullet is launched horizontally), the time is 0.48 seconds, and the acceleration due to gravity is approximately 9.8 m/s^2.

Plugging these values into the equation, we have:

distance = 0 * 0.48 s + (1/2) * 9.8 m/s^2 * (0.48 s)^2

Calculating this, we find that the vertical displacement of the bullet is approximately 0.56 meters.

Therefore, the bullet will miss the target by approximately 0.56 meters.