Question

A stone fell from the top of a cliff into the ocean. in the air, it had an average speed of \[16\] \[\text{m/s}\]. in the water, it had an average speed of \[3\] \[\text{m/s}\] before hitting the seabed. the total distance from the top of the cliff to the seabed is \[127\] meters, and the stone's entire fall took \[12\] seconds. how long did the stone fall in the air and how long did it fall in the water? the stone fell in the air for seconds and fell in the water for seconds.

Answer 1

The stone fell in the air for 7.9375 seconds and fell in the water for 4.0625 seconds.

Step-by-step explanation:

To solve this problem, we can break down the stone's fall into two parts: the fall in the air and the fall in the water.

First, let's find the time it took for the stone to fall in the air. We know that the total distance from the top of the cliff to the seabed is 127 meters and the average speed in the air is 16 m/s. Using the equation distance = speed x time, we can solve for time: 127 = 16 x time. Solving for time gives us time = 127/16 = 7.9375 seconds.

Next, let's find the time it took for the stone to fall in the water. We know that the stone had an average speed of 3 m/s in the water and the total time of the fall was 12 seconds. To find the time in the water, we subtract the time in the air from the total time: time in water = total time - time in air = 12 - 7.9375 = 4.0625 seconds.

Therefore, the stone fell in the air for 7.9375 seconds and fell in the water for 4.0625 seconds.