Understanding the Problem

* Horizontal Launch: The projectile is fired horizontally, meaning its initial vertical velocity is 0 m/s.

* Free Fall: Once the projectile leaves the gun, the only force acting on it is gravity, causing it to accelerate downwards.

Key Concepts

* Vertical Motion: We need to focus on the vertical component of the projectile's motion.

* Acceleration due to Gravity: The acceleration due to gravity (g) is approximately 9.8 m/s². This means the projectile's downward speed increases by 9.8 m/s every second.

* Constant Acceleration Equations: We can use the following equation to find the final vertical velocity:

* *v_f² = v_i² + 2ad*

Solution

1. Identify knowns:

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

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

* *d* (vertical distance) = 71.0 m

2. Plug the values into the equation:

* *v_f² = 0² + 2(9.8 m/s²)(71.0 m)*

* *v_f² = 1387.6 m²/s²*

3. Solve for the final vertical velocity (v_f):

* *v_f = √1387.6 m²/s² ≈ 37.2 m/s*

Answer

The magnitude of the vertical component of the projectile's velocity as it strikes the ground is approximately 37.2 m/s.