Consider that a coin is dropped into a wishing well. You want to determine the depth of the well from the time t between releasing the coin and hearing it hit the bottom. Suppose that t=2.059 s and assume the speed of sound in air is 330 m/s. What is the depth of the well?

Can someone please help, I cant get the right answer.

What I did was (0.5)(-9.80)(2.059^2)= 20.77m

But it is not correct and when I incorporate 330 m/s it gives me really big value.

You did it incorrectly.

The coin hits the water, then the sound comes up. You are given the total time.

Let t be total time, t1 be the time to fall, so t-t1 is the time for the sound to come up.

h=1/2*g*t1
h=vsound*(t-t1)
set these equal, and solve for t1, then go back and solve for h.

Well, well, well, looks like we've got ourselves a problem here. Don't worry, I'm here to help.

Now, it seems like you're on the right track using the formula for free fall to calculate the depth of the well. But it seems like you're missing a tiny detail. You see, sound takes time to travel up from the bottom of the well to your ears. So, we need to take that into account.

First, let's calculate how long it takes for the sound to reach your ears. We can use the formula: distance = speed × time. In this case, the distance is twice the depth of the well (since sound has to go down and then come back up), which we'll call "d".

So, 2d = 330 m/s × t. Let's plug in the values: 2d = 330 m/s × 2.059 s.

Now, let's solve for d: d = (330 m/s × 2.059 s) / 2.

Now, if we calculate that out, we get d = 339.747 m.

So, the depth of the well is approximately 339.747 meters. Just keep in mind that this calculation assumes no air resistance or other factors that might affect the speed of sound. Enjoy your wishing well adventures, my friend!

To determine the depth of the well, you need to consider the time it takes for the sound to travel back up to the top of the well. This means you need to calculate the total time it takes for the coin to fall and the sound to travel back up.

The formula for the distance fallen by an object in free fall is given by:
d = (1/2) * g * t^2

Where:
- d is the distance fallen
- g is the acceleration due to gravity (approximately 9.8 m/s^2)
- t is the time

In this case, we want to find the depth, which is the twice the distance fallen by the coin:
depth = 2 * d

Now, to calculate the total time it takes, we need to consider the time t it took to hear the sound. The time for the sound to travel back up the well is given by:
time_sound = depth / velocity_sound

Where:
- depth is the depth of the well
- velocity_sound is the speed of sound in air (330 m/s)

Since we have the equation for depth from earlier, we can substitute it into the equation for time_sound:
time_sound = (2 * d) / velocity_sound

Now, we can set up an equation to solve for d. We have the total time t and time_sound:
t = time_sound + time_coin

Rearranging the equation, we get:
t - time_sound = time_coin

Substituting the values given, we have:
2.059s - (2 * d) / 330m/s = d / 9.8m/s^2

Now we can solve for d. Let's rearrange the equation to isolate d on one side:
(2 * d) / 330m/s + d / 9.8m/s^2 = 2.059s

Simplifying the equation:
(2 * d) / 330 + d / 9.8 = 2.059

Finding a common denominator:
(2 * d * 9.8 + d * 330) / (330 * 9.8) = 2.059

Expanding the numerator:
(19.6d + 330d) / 3234 = 2.059

Combining like terms:
349.6d / 3234 = 2.059

Simplifying the equation further:
d = (2.059 * 3234) / 349.6

Evaluating the expression:
d ≈ 19.02 m

Therefore, the depth of the well is approximately 19.02 meters.

To find the depth of the well, you need to consider the time it takes for the sound to travel from the top of the well to the bottom and back up again, as well as the time it takes for the coin to fall.

First, let's calculate the time it takes for the sound to travel down to the bottom of the well and back up. Since the coin is dropped into the well, the sound will need to travel twice the depth of the well.

Using the formula distance = speed × time, we can write:

2 × depth = speed of sound × time
2 × depth = 330 m/s × 2.059 s
2 × depth = 679.77 m/s

Divide both sides by 2 to solve for the depth:

depth = 679.77 m/s ÷ 2
depth = 339.885 m.

So, the depth of the well is approximately 339.885 meters.

Your initial calculation of using the formula (0.5)(-9.80)(2.059^2) is correct for finding the distance the coin falls in a vacuum (ignoring air resistance). However, since the question mentions the speed of sound in air, we need to take the sound into account as well.