To determine the displacement of the rock, we need to consider its vertical motion separately during the upward and downward phases.
During the upward phase:
- Initial velocity (u) = 0 m/s (thrown straight upward)
- Final velocity (v) = ?
- Acceleration (a) = -9.8 m/s² (acceleration due to gravity)
- Displacement (s) = 10 m (height of the cliff)
We can use the following equation to find the final velocity:
v² = u² + 2as
Since the initial velocity (u) is 0:
v² = 0² + 2(-9.8)(10)
v² = -196
Taking the square root of both sides:
v ≈ -14 m/s
Note: The negative sign indicates that the velocity is directed opposite to the upward direction.
During the downward phase:
- Initial velocity (u) = -14 m/s (from the top of the cliff)
- Final velocity (v) = ?
- Acceleration (a) = -9.8 m/s² (acceleration due to gravity)
- Displacement (s) = -10 m (downward motion)
Using the same equation as before:
v² = u² + 2as
v² = (-14)² + 2(-9.8)(-10)
v² = 196 - 196
v ≈ 0 m/s
The final velocity in the downward phase is approximately 0 m/s since the rock reaches its peak height and starts falling back downward.
Now, to find the total displacement, we need to consider both phases. Since the displacement during the upward phase is positive (10 m) and the displacement during the downward phase is negative (-10 m), we can add them together:
Total displacement = 10 m - 10 m = 0 m
Therefore, the total displacement of the rock is 0 meters. It returns to the same vertical position from where it was thrown.