Final answer:
Both spheres shot horizontally from a height of 2m will reach the ground at the same time because the horizontal velocity does not influence the vertical fall time, only gravity does.
Step-by-step explanation:
In projectile motion, the time it takes for an object to reach the ground is dependent only on the vertical component of its motion. When two spheres are shot horizontally from the same height, regardless of their horizontal velocities, they will reach the ground at the same time assuming there's no air resistance. This is because the horizontal motion does not affect the time it takes to fall the given vertical distance due to gravity.
To illustrate further, whether a sphere is shot at 5 m/s or 10 m/s horizontally from a height of 2m, they both have an initial vertical velocity of 0 m/s, and they are both subjected to the same gravitational acceleration of approximately 9.8 m/s2. Therefore, they will touch the ground simultaneously since gravity acts on them equally.