A rock is dropped from a sea cliff, and the sound of it striking the ocean is heard 3.2 s later. If the speed of sound is how high is the cliff?

Missing data.

1000m

No

To determine the height of the cliff, we need to calculate the time it takes for the rock to fall and compare it with the time it takes for the sound to reach the observer.

First, let's break down the problem into two parts:
1. Time taken by the rock to fall from the cliff to the ocean.
2. Time taken by the sound to travel from the ocean back to the observer.

1. Time taken by the rock to fall:
We can make use of the equation of motion for free-falling objects:
h = (1/2) * g * t^2

Where:
h is the height of the cliff,
g is the acceleration due to gravity (approximately 9.8 m/s^2),
t is the time taken by the rock to fall.

Given that it takes 3.2 seconds for the sound to be heard, we can assume that it takes the same time for the rock to fall. Thus, we can substitute the given time (t) into the equation to find the height (h).

2. Time taken by the sound to travel:
The speed of sound is given as a constant, but we need to distinguish the time taken by the sound to reach the observer. Since the sound traveled from the ocean to the observer, we can divide the total distance covered by the speed of sound to find the time taken.

Now, let's calculate the height of the cliff step by step:

1. Calculating time taken by the rock to fall:
h = (1/2) * g * t^2
h = (1/2) * (9.8 m/s^2) * (3.2 s)^2
h = (1/2) * 9.8 m/s^2 * 10.24 s^2
h = 49.056 m

2. Calculating time taken by the sound to travel:
Since the sound travels back from the ocean to the observer, it covers double the distance the rock fell. Therefore, we multiply the time it took for the sound to be heard, 3.2 seconds, by 2.
t_sound = 3.2 s * 2
t_sound = 6.4 s

Next, we divide the time taken by the sound (t_sound) by the speed of sound (v_sound) to find the distance covered:
distance = speed * time
distance = v_sound * t_sound

Assuming the speed of sound is approximately 343 m/s (at sea level and room temperature), we can calculate the distance traveled by the sound:
distance = 343 m/s * 6.4 s
distance = 2195.2 m

3. Calculating the height of the cliff:
Since the sound traveled the same distance as the rock fell, the height of the cliff is equal to the distance covered by the sound:
height = distance
height = 2195.2 m

Therefore, the height of the cliff is approximately 2195.2 meters.