To determine the horizontal distance the stone travels before striking the ground, we need to find the time it takes for the stone to fall and then multiply it by the horizontal velocity.
Since the stone is thrown horizontally, its initial vertical velocity is 0 ft/s. The only force acting on the stone in the vertical direction is gravity. The height of the cliff (100 ft) can be considered as the vertical displacement.
We can use the kinematic equation for vertical motion:
h = ut + (1/2)gt^2
Where: h = vertical displacement (100 ft) u = initial vertical velocity (0 ft/s) g = acceleration due to gravity (32.2 ft/s^2) t = time
Plugging in the values, we get:
100 = 0t + (1/2)32.2t^2 100 = 16.1t^2 t^2 = 100/16.1 t^2 = 6.21118 t ≈ √6.21118 t ≈ 2.49 seconds (rounded to two decimal places)
Now that we have the time it takes for the stone to fall, we can calculate the horizontal distance traveled using the formula:
distance = velocity * time
The initial horizontal velocity is 20 ft/s, and the time is 2.49 seconds.
distance = 20 ft/s * 2.49 s distance ≈ 49.8 ft
Therefore, the stone strikes the ground approximately 49.8 ft from the base of the cliff.