Final answer:
The height of the cliff can be calculated using the equations of motion. By applying the equation h = (1/2)gt^2, we can solve for the height of the cliff as 19.6 m. Therefore, the closest option is c - 100 m.
Step-by-step explanation:
The height of the cliff can be calculated using the equations of motion. Since the stone is thrown horizontally, its initial vertical velocity is 0 m/s. The only force acting on the stone in the vertical direction is gravity (9.8 m/s^2), which causes it to accelerate downward. We can use the equation h = (1/2)gt^2 to relate the height of the cliff (h) to the time it takes for the stone to hit the water (t).
Plugging in the values:
- g = 9.8 m/s^2 (acceleration due to gravity)
- t = 2.0 s (time taken to hit the water)
We can rearrange the equation to solve for h: h = (1/2)gt^2.
Substituting the given values, we get h = (1/2)(9.8 m/s^2)(2.0 s)^2 = 19.6 m.
Therefore, the height of the cliff is closest to 19.6 m, which corresponds to option c.