A spelunker drops a stone from rest into a hole. The speed of sound is 343m/s in air, and the sound of the stone striking the bottom is heard 1.46s after the stone is dropped. How deep is the hole? What is it in meters
time=time down + time up
time=sqrt(2h/g)+ h/vsound
solve for time Use the quadratic equation.
Solve the equation
t1 + t2 =
(stone's time required to fall) + (time to hear the splash) = 1.46 s
(1/2) g t1^2 = H
t1 = sqrt (2H/g)
a H = t2 (a is the sound speed, 343 m/s)
t2 = H/a
You will have to set it up as a quadratic equation in H, the depth of the well.
10.24
a stone is dropped into a well . The sound of the splash is heard 30s after the stone is dropped . What is the depth of the well? Note that the speed of sound in air is 343m / s.
To find the depth of the hole, we first need to determine the time it takes for the stone to reach the bottom. We can then use this time to calculate the depth of the hole.
Given that the speed of sound in air is 343 m/s, and the sound of the stone striking the bottom is heard 1.46 seconds after the stone is dropped, we can conclude that the time it takes for the sound to travel from the bottom to the top of the hole is also 1.46 seconds.
Since the sound travels from the bottom to the top of the hole and then back down to the bottom, the total travel time for the sound is twice that of the time it took to hear the sound (2 * 1.46 seconds = 2.92 seconds).
Now, we can calculate the time it took for the stone to reach the bottom of the hole by subtracting the time it took for the sound to travel from the total travel time of the sound. The time for the stone to fall can be calculated as follows:
Time for the stone to fall = Total travel time of sound - Time for sound to travel
Time for the stone to fall = 2.92 seconds - 1.46 seconds = 1.46 seconds
Now, we can use the equation for the distance fallen by an object under free fall:
Distance = (1/2) * acceleration due to gravity * time^2
Assuming the acceleration due to gravity is approximately 9.8 m/s^2, we can calculate the distance:
Distance = (1/2) * 9.8 m/s^2 * (1.46 seconds)^2
Distance = 1/2 * 9.8 m/s^2 * 2.1316 s^2
Distance = 10.04312 meters
Therefore, the depth of the hole is approximately 10.04312 meters.