Final answer:
The ball will hit the ground approximately 24.48 meters from the base of the cliff.
Step-by-step explanation:
The ball is thrown horizontally, which means it has an initial vertical velocity of 0 m/s. Using the equation h = ut + 0.5gt^2, where h is the vertical displacement, u is the initial vertical velocity, t is the time, and g is the acceleration due to gravity, we can solve for the time it takes for the ball to hit the ground. Since the ball is thrown horizontally, the initial vertical velocity is 0, resulting in the equation:
80 = 0 * t + 0.5 * (-9.8) * t^2
Simplifying the equation, we get:
4.9t^2 = 80
t^2 = 80 / 4.9
t ≈ 4.08 seconds
Now that we know the time, we can use the equation d = ut, where d is the horizontal distance, u is the initial horizontal velocity, and t is the time:
d = 6.0 * 4.08
d ≈ 24.48 meters
Therefore, the ball will hit the ground approximately 24.48 meters from the base of the cliff.