Understanding the Problem

* Projectile Motion: We're dealing with an object launched horizontally from a height. This means it has both vertical and horizontal motion.

* Vertical Motion: The object falls vertically due to gravity.

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

Key Concepts

* Vertical Motion:

* Acceleration due to gravity (g) = 9.8 m/s²

* Initial vertical velocity (v₀y) = 0 m/s (since the object is launched horizontally)

* Horizontal Motion:

* Velocity (vₓ) is constant.

Solution

1. Vertical Motion:

* Find the time it takes to fall 5 meters:

* Use the equation: d = v₀yt + (1/2)gt²

* 5 = 0 * t + (1/2) * 9.8 * t²

* t² = 5/4.9

* t = √(5/4.9) ≈ 1 second

2. Final Velocity:

* The final velocity is the vector sum of the horizontal and vertical velocities.

* Horizontal Velocity (vₓ): We don't have enough information to calculate this. We need to know the initial horizontal velocity or the time it took to travel 10 meters horizontally.

* Vertical Velocity (vᵧ):

* Use the equation: vᵧ = v₀y + gt

* vᵧ = 0 + 9.8 * 1

* vᵧ = 9.8 m/s

Answer

* We can't determine the final velocity without knowing the initial horizontal velocity or the time it took to travel 10 meters horizontally.

* However, we can say that the vertical component of the final velocity is 9.8 m/s.

To find the full final velocity, you would need additional information about the horizontal motion.