Final answer:
To find the horizontal velocity needed for the water balloon to hit the cat, calculate the time it takes to fall 13 meters vertically due to gravity, then divide the horizontal distance by that time to find the required horizontal velocity.
Step-by-step explanation:
To calculate the horizontal velocity with which Liam should throw the water balloon to hit the neighborhood cat, we need to consider projectile motion. Since the vertical motion (due to gravity) and horizontal motion (due to initial velocity) are independent, we can treat them separately. Assuming there is no air resistance, the horizontal velocity is constant. Therefore, the time it takes for the water balloon to hit the ground is only dependent on the vertical distance and the acceleration due to gravity. First, we find the time (t) it takes for the water balloon to fall 13 meters using the formula dy = 1/2 * g * t^2, where dy is the vertical distance, and g is the acceleration due to gravity (approximately 9.81 m/s^2). Rewriting this formula to solve for t gives us t = sqrt(2 * dy/g). Plugging in the values, we get t = sqrt(2 * 13 m / 9.81 m/s^2), which we can calculate. Next, with the time known, we determine the required horizontal velocity (vx) to ensure the water balloon travels 9 meters horizontally during the same time frame using the formula vx = dx/t, where dx is the horizontal distance. Therefore, vx = 9 m / t. Finally, after calculating the time, we'll use that value to find the necessary horizontal velocity for the water balloon to reach the cat.