Final answer:
To find the velocity and position functions of the rock, integrate the acceleration function to get the velocity function and integrate the velocity function to get the position function. The time the rock hits the ground can be found by setting the position function equal to the height of the cliff and solving for t. The velocity of the rock at the time it hits the ground can be found by plugging in the time into the velocity function.
Step-by-step explanation:
To find the velocity and position functions of the rock, we can use the equations of motion for a falling object. The velocity function can be found by integrating the acceleration function, which in this case is the acceleration due to gravity. The position function can be found by integrating the velocity function.
The acceleration due to gravity is constant at -9.8 m/s^2. Integrating this gives us the velocity function, v(t) = -9.8t + v0, where v0 is the initial velocity of the rock.
Integrating the velocity function gives us the position function, s(t) = -4.9t^2 + v0t + s0, where s0 is the initial position of the rock.
The time at which the rock hits the ground can be found by setting the position function equal to the height of the cliff, which is -300 meters. Solving for t gives us t = (-v0 - sqrt(v0^2 - 4(-4.9)(-300))) / (2(-4.9)).
The velocity of the rock at the time it hits the ground can be found by plugging in the time into the velocity function.