Final answer:
The height of the water droplet above the cave floor after 3 seconds, based on the equation provided, cannot be determined as the droplet would have already hit the ground. By solving the equation, it is found that the droplet would have hit the ground at approximately 2.12 seconds, before the 3-second mark.
Step-by-step explanation:
The question relates to the height of a water droplet that falls from a stalactite in a cave, which is given by the quadratic expression 22 - 4.9t², where t is the time in seconds. To find the height after 3 seconds, we substitute t with 3 and calculate the expression:
22 - 4.9(3)² = 22 - 4.9(9) = 22 - 44.1 = -22.1.
However, the negative result indicates that our reference point of 22 meters is not accurate at time t=3 seconds because the droplet would have already hit the ground.
Instead, we must determine the last time at which the droplet was at or above the ground level before reaching 3 seconds. By setting the height to zero (0 = 22 - 4.9t²), we can solve for t and ascertain the time it hits the ground before 3 seconds:
4.9t² = 22
t² ≈ 4.49
t ≈ 2.12 seconds.
Since the time to hit the ground is less than 3 seconds, the answer we seek must be invalid, as the droplet would no longer be in the air to measure its height at 3 seconds.