Understanding the Problem

* Horizontal Motion: The bullet travels horizontally at a constant speed.

* Vertical Motion: The bullet is affected by gravity, causing it to fall downwards.

* Goal: We need to find the distance the bullet travels horizontally before hitting the ground.

Key Concepts

* Projectile Motion: The bullet's motion is an example of projectile motion, where an object is launched with an initial velocity and follows a curved path.

* Uniform Motion: The horizontal component of the bullet's motion is uniform, meaning it travels at a constant speed.

* Free Fall: The vertical component of the bullet's motion is free fall, meaning it's only affected by gravity.

Solution

1. Finding the Time of Flight: The time it takes for the bullet to hit the ground depends on its vertical motion. Since the bullet is fired horizontally, its initial vertical velocity is 0 m/s. We can use the following kinematic equation:

* d = v₀t + (1/2)at²

* d = vertical distance (we need to know this, which is the height of the rifle above the ground)

* v₀ = initial vertical velocity (0 m/s)

* a = acceleration due to gravity (9.8 m/s²)

* t = time of flight (what we want to find)

We need the height of the rifle to solve for 't'.

2. Finding the Horizontal Distance: Once we know the time of flight ('t'), we can use the following equation to calculate the horizontal distance:

* d = vt

* d = horizontal distance (what we're looking for)

* v = horizontal velocity (790 m/s)

* t = time of flight (calculated in step 1)

Important Note: The observer's distance of 26 meters is irrelevant to this problem. The observer's position is only relevant if we want to calculate the angle at which the observer sees the bullet hit the ground.

Let me know if you can provide the height of the rifle above the ground. Then I can calculate the distance the bullet travels!