Final answer:
To find the final velocity of a rock dropped from a cliff, we use two kinematic equations. However, the exact final velocity cannot be determined from the options provided (a, b, c, d) after calculating using the correct physics formulas for freely falling objects.
Step-by-step explanation:
The question is regarding the final velocity of a rock that is dropped from a height. To determine the velocity just before the rock hits the ground, we will use the following physics equation for free-falling objects:
v = u + at
where:
- v is the final velocity
- u is the initial velocity (which is 0 m/s because the rock is dropped)
- a is the acceleration due to gravity (9.8 m/s2)
- t is the time taken to hit the ground
Since we are not given the time, we can use another equation to find time by first finding the displacement (s):
s = ut + \(\frac{1}{2}\)at2
By rearranging and solving for time, we find that:
t = \(\sqrt{\frac{2s}{a}}\)
Using the displacement s of 100 m and a of 9.8 m/s2:
t = \(\sqrt{\frac{2 \times 100}{9.8}}\)
After calculating t, we substitute it back into the first equation to solve for v, the final velocity.
Therefore, the correct answer is not provided in the options given if we calculate v using the correct physics formulas.