A rock is dropped from a sea cliff and the sound of it striking the ocean is heard 4.1s later. If the speed of sound is B40 m/s, how high is the cliff? ____m
Well, if you're dropping rocks off cliffs, I hope you're not doing it just for rocks and giggles! Let's calculate the height of the cliff with a splash of humor.
We know that the time it takes for the sound to reach us is 4.1 seconds. But it's not polite to keep an ocean waiting, so the rock was in a hurry to meet its water friends!
Now, the speed of sound is about 343 m/s. That's pretty fast, but not as fast as the rumors that spread in a beauty salon, trust me.
To find the height of the cliff, we need to multiply the speed of sound by the time it took for the sound to reach us. I'll do the math quietly, so I don't disturb anyone's beauty sleep.
Height of cliff = Speed of sound × Time taken
Height of cliff = 343 m/s × 4.1 s
Ta-da! The height of the cliff is approximately 1402.3 meters. That's high enough to tickle the clouds and make seagulls jealous!
To determine the height of the cliff, we can use the formula:
height = (1/2) * gravity * time^2
We know the time it took for the sound to reach us, which is 4.1 seconds. However, we need to first determine the time it took for the rock to fall to the ocean's surface.
Since the sound travels at a finite speed, we need to subtract the time it took for the sound to reach us from the total time it took for the rock to fall.
Let's calculate the time it took for the rock to fall to the ocean's surface:
falling time = total time - sound travel time
falling time = 4.1s - 0s (since sound travels instantaneously)
Now we can use the falling time to calculate the height of the cliff:
height = (1/2) * gravity * falling time^2
The acceleration due to gravity is approximately 9.8 m/s^2. Let's substitute the values into the formula:
height = (1/2) * 9.8 m/s^2 * (4.1s - 0s)^2
height = (1/2) * 9.8 m/s^2 * 4.1s^2
height = 0.5 * 9.8 m/s^2 * 16.81s^2
height = 81.899 m
Therefore, the height of the cliff is approximately 81.899 meters.
To find the height of the cliff, we can use the equation of motion for the falling rock. The time it takes for the rock to reach the surface of the ocean is equal to the time it takes for the sound of the impact to travel back up to the top of the cliff.
Let's break down the process step by step:
Step 1: Calculate the time it takes for the rock to fall.
We know that the time it takes for the sound to travel back up is 4.1 seconds. Since sound travels at a constant speed of 340 m/s, we can use the formula:
Distance = Speed × Time
To find the distance, we rearrange the formula as:
Time = Distance / Speed
Given that Time = 4.1 seconds and Speed = 340 m/s, we can calculate the distance traveled by sound:
Distance = 4.1 seconds × 340 m/s
Step 2: Calculate the distance traveled by the rock.
Since the sound takes 4.1 seconds to travel back up to the top of the cliff, the rock takes the same amount of time to fall. We can use the formula for free-fall motion:
Distance = (1/2) × Acceleration × Time^2
The acceleration due to gravity is approximately 9.8 m/s^2.
Distance = (1/2) × 9.8 m/s^2 × (4.1 seconds)^2
Step 3: Calculate the height of the cliff.
The height of the cliff is equal to the sum of the distances traveled by sound and the rock. Therefore:
Height = Distance (rock) + Distance (sound)
Height = [(1/2) × 9.8 m/s^2 × (4.1 seconds)^2] + [4.1 seconds × 340 m/s]
Calculating this expression will give you the height of the cliff.