Final answer:
Using equations of motion, we can calculate the time it takes for the ball to fall to the ground and the horizontal distance it travels. The height of the cliff can be found by using the equation h = (1/2) * g * t^2. The horizontal velocity of the ball is approximately 10.3 m/s.
Step-by-step explanation:
To solve this problem, we can use the equations of motion. Since the ball is launched horizontally, its initial vertical velocity is 0 m/s. First, we can use the equation h = (1/2) * g * t^2 to find the time it takes for the ball to fall to the ground, where h is the height, g is the acceleration due to gravity (9.8 m/s^2), and t is the time.
Rearranging the equation to solve for t, we get t = sqrt(2h / g). Plugging in the given height of the cliff, we get t = sqrt(2 * h / g) = sqrt(2 * 22 / 9.8) ≈ 2.13 s.
Next, we can use the equation d = v * t to find the horizontal distance the ball travels, where d is the distance, v is the horizontal velocity, and t is the time. Rearranging the equation to solve for v, we get v = d / t. Plugging in the given horizontal distance and the calculated time, we get v = d / t = 22 / 2.13 ≈ 10.3 m/s.
Therefore, the horizontal velocity of the ball is approximately 10.3 m/s.