Final answer:
To find the time it takes for a rock dropped from rest to fall -64.1 meters, we use the kinematic equation taking into account the initial velocity of 0 m/s and the acceleration of gravity. Solving for time, we can determine how long it takes to hit the ground.
Step-by-step explanation:
You asked how long it takes for a rock to hit the ground when it's dropped from rest from a height of -64.1 m. To solve this problem, we can use the kinematic equation for objects in free fall:
y = v_i*t + (1/2)*a*t^2
Where y is the displacement, v_i is the initial velocity (0 m/s in this case since the rock starts from rest), a is the acceleration due to gravity (-9.8 m/s^2), and t is the time in seconds. Since the rock is dropped from rest, v_i is 0 m/s. Plugging in the values:
-64.1 m = 0 m/s * t + (1/2) * (-9.8 m/s^2) * t^2
By solving for t, we can determine the time it takes for the rock to reach the ground. The displacement y is negative because the rock falls below its initial position.