Final answer:
The horizontal position of the mouse when it has fallen 12.0 m is approximately 5.46 meters.
Step-by-step explanation:
To determine the horizontal position of the mouse when it has fallen 12.0 m, we need to consider the vertical motion of the mouse. We can use the formulas of projectile motion to solve this problem. First, we can calculate the time it takes for the mouse to fall 12.0 m using the formula: h = (1/2) * g * t^2. Substituting the given values, we get: 12.0 = (1/2) * 9.8 * t^2, which simplifies to t^2 = 2.449 and t = 1.56 s.
Next, we can find the horizontal distance traveled by the mouse using the formula: d = v * t, where v is the horizontal velocity of the owl. Substituting the given values, we get: d = 3.50 * 1.56 = 5.46 m.
Therefore, the horizontal position of the mouse when it has fallen 12.0 m is approximately 5.46 meters.