You drop a stone down a well that is 12.37 m deep. How long is it before you hear the splash? The speed of sound in air is 343 m/s.

let t1 be the fall time, t2 be the time for sound coming back up. You want t1+t2

t1:
12.37=1/2 g (t1)^2 solve for t1
t2:
12.37=343*t2 solve for t2

To find out how long it takes for you to hear the splash after dropping the stone, we need to calculate the time it takes for the sound of the splash to travel up from the bottom of the well to your ears.

First, let's find the time it takes for the stone to fall to the bottom of the well. We can use the formula for the time it takes for an object to fall freely (neglecting air resistance):

t = sqrt(2h / g)

where:
t is the time it takes to fall,
h is the height of the well (12.37 m in this case), and
g is the acceleration due to gravity (approximately 9.8 m/s^2).

Substituting the values:

t = sqrt(2 * 12.37 / 9.8)

Now, let's calculate the time it takes for the sound to travel up the well. The speed of sound in air is given as 343 m/s.

t_sound = d / v

where:
t_sound is the time for the sound to travel,
d is the distance (or depth of the well, which is 12.37 m), and
v is the speed of sound in air (343 m/s).

Substituting the values:

t_sound = 12.37 / 343

Finally, to find the total time it takes for you to hear the splash, we need to add the time it takes for the stone to fall and the time it takes for the sound to reach your ears:

total_time = t + t_sound

Simply perform the calculations to find the answer.