Final answer:
To determine the time the rock is in the air, we can use the formula for horizontal motion and the formula for falling objects. By substituting the given values and using appropriate formulas, we find that the rock is in the air for approximately 2.55 seconds.
Step-by-step explanation:
To determine the time the rock is in the air, we can use the formula for horizontal motion. Since the rock is kicked horizontally, its initial vertical velocity is 0 m/s. The displacement in the vertical direction is equal to the height of the cliff, H. We can use the formula h = (1/2)gt^2 to find the time, t, it takes for the rock to fall to the ground.
Given that the rock is kicked horizontally at a speed of 16 m/s and hits the ground 65 m from the foot of the cliff, we can calculate the time it takes for the rock to fall. The horizontal distance travelled by the rock is equal to its horizontal velocity, which is constant, multiplied by the time it takes to fall. Using the formula d = vt, where d is the distance and t is the time, we can solve for t.
Since the rock is kicked horizontally, it will take the same amount of time to fall as if it were dropped straight down from the cliff. Therefore, we can use the formula t = sqrt(2h/g) to find the time it takes for the rock to fall. Substituting the given values, we find that the rock is in the air for approximately 2.55 seconds.