On a 28°C summer day, you decide to go cliff diving with some friends. Your friend jumps first and you notice that it takes 2 seconds for you to hear them splash into the water below. How high is the cliff?
To calculate the height of the cliff, we need to find the time it takes for the sound to reach the jumper's ears after they have jumped and fallen from the cliff.
The speed of sound in air is approximately 343 meters per second at 28°C.
Since the sound takes 2 seconds to reach you, the total time for the sound to travel back and forth from the jumper to you is 2 seconds.
Therefore, the time it takes for the sound to reach the jumper after they have jumped and fallen can be calculated by subtracting the time it takes for the sound to reach you from the total time.
So, the time taken by the sound to reach the jumper can be calculated as 2 seconds - 2 seconds = 0 seconds.
Since the time is zero seconds, it means that the sound reaches the jumper instantaneously.
Now, let's calculate the height of the cliff using the equation:
Height = (speed of sound × time taken by sound to reach you) / 2
Height = (343 m/s × 2 s) / 2
Height = 686 meters / 2
Height ≈ 343 meters
Therefore, the height of the cliff is approximately 343 meters.