Since the ball is thrown horizontally, its initial velocity in the vertical direction is zero. The only force acting on the ball in the vertical direction is gravity. We can use the kinematic equation for vertical motion to determine the time it takes for the ball to fall from the cliff:
h = (1/2) * g * t^2
Where: h = vertical displacement (100 meters) g = acceleration due to gravity (9.8 m/s^2) t = time
By rearranging the equation, we can solve for t:
t^2 = (2 * h) / g t^2 = (2 * 100) / 9.8 t^2 = 20.408 t ≈ √20.408 t ≈ 4.52 seconds
Now that we have the time it takes for the ball to fall, we can find the horizontal distance it travels. Since the initial velocity in the horizontal direction is 20 m/s, and there is no acceleration horizontally (assuming negligible air resistance), the horizontal distance can be calculated using the formula:
d = v * t
Where: d = horizontal distance v = horizontal velocity (20 m/s) t = time (4.52 seconds)
Plugging in the values, we get:
d = 20 * 4.52 d ≈ 90.4 meters
Therefore, the ball will land approximately 90.4 meters from the base of the cliff.