Final answer:
To determine how long it takes a rock to fall 30.0 meters, we use the equation of motion s = ut + 1/2 at^2. With initial velocity u being zero and 'a' as the acceleration due to gravity, we find the time 't' to be apaproximately 2.47 seconds.
Step-by-step explanation:
To calculate the time it takes for a rock to hit the ground from a certain height, one can use the kinematic equations of motion under the influence of gravity. The key equation we will use is:
s = ut + 1/2 at^2
Where:
- s is the displacement (height from which the rock is dropped)
- u is the initial velocity (0 m/s if the rock is simply dropped)
- a is the acceleration due to gravity (9.8 m/s^2 on Earth)
- t is the time in seconds
For a rock dropped from a height of 30.0 meters, the equation considering u = 0 becomes:
30.0 = 0 * t + 1/2 * 9.8 * t^2
Solving this quadratic equation for t, we get:
t^2 = (2 * 30.0) / 9.8
t^2 = 6.12244897959
t = sqrt(6.12244897959)
t ≈ 2.47 seconds
So, the rock takes approximately 2.47 seconds to hit the ground.