A stone is dropped from the deck of the bridge. The sound of the splash reaches the deck 3 seconds later. If sound travels at 342 m/s in still air, how high is the deck of bridge above the water?
the falling time can be found by:
h-4.9t^2 = 0
t = √(h/4.9)
echo time is h/342, so
√(h/4.9) + h/342 = 3.0
h = 40.673 meters
Well, if we take the drop of the stone and the sound of the splash into account, it's safe to say that there was quite a delay. It's almost like they were playing a game of Marco Polo, but with more physics involved.
Now, let's get down to the numbers. We know that sound travels at approximately 342 m/s in still air, and it took 3 seconds for the sound to make its way to the deck. So, if we use a little bit of math magic, we can calculate that the distance from the water to the deck is around 1026 meters.
So there you have it - the height of the deck above the water is approximately 1026 meters. The stone must have had quite a thrilling free fall!
To find the height of the deck of the bridge above the water, we can use the equation:
\[ h = \frac{1}{2} g t^2 \]
where:
- h is the height (in meters)
- g is the acceleration due to gravity, approximately 9.8 m/s^2
- t is the time it takes for the stone to hit the water (in seconds)
Given that the sound of the splash reaches the deck 3 seconds later, we can assume that it took the stone 3 seconds to hit the water.
Substituting the values into the equation, we have:
\[ h = \frac{1}{2} \times 9.8 \times (3)^2 \]
Simplifying the equation, we get:
\[ h = \frac{1}{2} \times 9.8 \times 9 \]
Finally, we can calculate the height:
\[ h = 44.1 \, \text{meters} \]
Therefore, the deck of the bridge is approximately 44.1 meters above the water.
To calculate the height of the deck of the bridge above the water, we need to consider the time it takes for the stone to fall and the time it takes for the sound to travel back up from the water to the deck.
First, let's calculate the time it took for the stone to fall before hitting the water. We can use the equation of motion:
s = ut + (1/2)gt^2
where s is the distance, u is the initial velocity, g is the acceleration due to gravity (approximately 9.8 m/s^2), and t is the time.
Since the stone is dropped, its initial velocity (u) is 0 m/s. Setting s equal to the height of the deck, we get:
h = (1/2)gt^2
Plugging in the values, we have:
h = (1/2)(9.8 m/s^2)(3 s)^2
h = (1/2)(9.8 m/s^2)(9 s^2)
h = 44.1 m
Therefore, the height of the deck of the bridge above the water is 44.1 meters.