While stationary on a boat you are measuring the time it takes for the coin to leave your hand and hit the water.In order to measure that time you are tuned to the sound of the coin hitting the water. You know that it takes 5.5 seconds for the coin to leave your hand and hit the water but the timer that you are using shows 6 seconds. What is the distance between your hand and the water surface? What is the speed of sound in this case?
The extra 0.5 seconds is the time it takes for the sound of the splash to reach you.
The height of the hand above the water surface is
(1/2)gt^2 = (4.9)(5.5)^2 = 148 m.
The speed of sound is 148/0.5 = 296 m/s
To find the distance between your hand and the water surface, and the speed of sound, we can use the given information along with the formula for distance:
Distance = Speed × Time
Let's break it down step by step.
1. First, let's find the actual time it took for the coin to leave your hand and hit the water. You know that your timer shows 6 seconds, but the actual time is 5.5 seconds. So, there is a time difference of 0.5 seconds.
2. Now, we'll use the actual time (5.5 seconds) to calculate the distance between your hand and the water surface. To do this, we need to know the speed of sound.
3. Speed of sound is the rate at which sound travels through a medium. It varies depending on various factors like temperature, humidity, and the medium it is traveling through. For simplicity, let's assume the speed of sound in air at room temperature is approximately 343 meters per second.
4. Using the formula for distance, Distance = Speed × Time, we can substitute the known values: Distance = 343 m/s × 5.5 s.
Calculating this, we find that the distance between your hand and the water surface is:
Distance = 343 m/s × 5.5 s = 1886.5 meters.
So, the distance between your hand and the water surface is approximately 1886.5 meters.
Now, let's find the speed of sound in this case.
As mentioned earlier, the speed of sound is typically around 343 m/s, but it can vary based on environmental conditions, including temperature and humidity. If the speed of sound in this case were different from the assumed 343 m/s, we would need additional information to determine it precisely.