To find the horizontal distance the stone will travel before striking the ground, we can use the equations of motion. Since the stone is thrown horizontally, its initial vertical velocity is 0 m/s, and it will only be affected by the vertical acceleration due to gravity (9.8 m/s²).
We can use the equation of motion for vertical displacement:
h = ut + (1/2)gt²
Where: h = vertical displacement (negative since it's downward in this case) u = initial vertical velocity (0 m/s) g = acceleration due to gravity (9.8 m/s²) t = time of flight
Since the stone is thrown horizontally, the time of flight will be the same as if it was dropped from the same height. We can find the time of flight using the equation:
h = (1/2)gt²
Rearranging the equation, we get:
t² = 2h / g
Substituting the values, we have:
t² = 2 * 80 m / 9.8 m/s² t² = 16.3265 s² t ≈ 4.04 s
Now that we have the time of flight, we can find the horizontal distance traveled using the equation:
d = ut
Where: d = horizontal distance u = initial horizontal velocity (10 m/s)
Substituting the values, we have:
d = 10 m/s * 4.04 s d ≈ 40.4 m
Therefore, the stone will strike the ground approximately 40.4 meters from the base of the cliff.