To determine how far from the base of the cliff the ball will land, we can use the equations of motion. Since the ball is thrown horizontally, its initial vertical velocity is 0 m/s.
We can use the following equation to calculate the time it takes for the ball to reach the ground:
h = (1/2) * g * t^2
where h is the initial height (20 m), g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.
Plugging in the values, we have:
20 = (1/2) * 9.8 * t^2
Simplifying the equation, we get:
t^2 = 20 * 2 / 9.8 t^2 = 40 / 9.8 t^2 ≈ 4.08
Taking the square root of both sides, we find:
t ≈ √4.08 t ≈ 2.02 s
Now that we know the time it takes for the ball to reach the ground, we can calculate the horizontal distance traveled using the equation:
d = v * t
where d is the horizontal distance, v is the horizontal velocity (5 m/s), and t is the time (2.02 s).
Plugging in the values, we have:
d = 5 * 2.02 d ≈ 10.1 m
Therefore, the ball will land approximately 10.1 meters from the base of the cliff.